When the original Japanese professional wrestling organization, the JWA, dissolved in the early 1970s, its top two stars, Antonio Inoki and Giant Baba, formed their own promotions that presented each man's vision of professional wrestling. Inoki created New Japan Pro Wrestling and developed "Strong Style" while Baba founded All Japan Pro Wrestling and defined his promotion's style as "King's Road."
STRONG STYLE
First lets talk about Strong Style. It is the most common word used to describe the type of wrestling performed in New Japan, which is the largest federation in the country and second largest in the world. The title "Strong Style" itself describes New Japan's philosophy and the philosophy of its founder, Antonio Inoki. New Japan refers to itself as the "King of Sports," so in their eyes it must also have the strongest style of fighting. New Japan's style isn't static, but over the years has taken elements from other types of wrestling and incorporated it into their style.
Today, Strong style means hard-hitting New Japan matches, basically. It incorporates submission finishes more frequently than "King's Road", as Inoki's vision was Pro Wrestling as a Mixed Martial Art. You are more apt to see a quick cross armbreaker (jujigatame) finish in New Japan, as the move is established as a very dangerous submission that many times results in an instant tap-out. The three different representatives of Strong Style throughout New Japan's existence were Inoki himself, Riki Choshu, and then Shinya Hashimoto in the 1990s. Since Hashimoto left the company New Japan really hasn't gotten a "stylistic leader" or true "ace" at the level of those three men, but has pinned its hopes on the current top wrestlers Shinsuke Nakamura and Hiroshi Tanahashi.
When New Japan first opened up in the 1970s there was a heavy emphasis on a long portion of early matwork, a legacy that lives on today. Inoki would regularly work holds for an extended period of time and then turn it on for a big finish with high impact moves like the dropkick and suplexes. In later years when matwork as the major vehicle for telling stories fell by the wayside, this type of structure often lead to big New Japan matches featuring cursory matwork in the beginning of the match that didn't really play into the later portions, where they seemed to start the "real match" and bring out their hard hitting arsenal. Inoki's vision of pro wrestling presented it as a style of fighting, to be put up against other martial arts disciplines like judo and karate. This lead to him working in many "different style fights" against top practitioners of other fighting styles; worked matches, mind you, that Inoki used to put himself and pro wrestling as a whole over. Inoki would later lose sight of that goal with the later MMA-influence movement that came on the heels of PRIDE's success, but that is another topic for another time.
Strong Style took a turn for the faster paced when Riki Choshu turned heel and started up the Ishigundan (Restruction Force), an anti-establishment faction that looked to topple the Inoki/Fujinami hierarchy of New Japan's Seikigun (regular army). Choshu and his compatriots - hard-working veterans Masa Saito and Killer Khan, the young Yoshiaki Yatsu and the little spitfire Animal Hamaguchi - brought rapid-fire double and triple team moves to their matches and a more brisk pace in between periods of inactivity with restholds like the Figure 4 Headscissor.
Another contributing influence to "Strong Style" was the formation of the UWF by breakaway stars like Yoshiaki Fujiwara, Osamu Kido, and the young Akira Maeda. The UWF group stressed more realistic "fighting" in their wrestling and pushed clean finishes (a concept that was directly against most booking in Japan at the time as even tournament finals and title matches often ended in screwjob finishes to protect the wrestlers from losing outright). When UWF version 1 closed its doors, many of the wrestlers came back to New Japan and ran an "invasion" angle, where their "kick suplex and submission" style really caught on with the fans and began to be incorporated into New Japan matches. A classic match in the tradition of the two colliding styles was Akira Maeda vs. Tatsumi Fujinami from June 12, 1986.
Upon Choshu's return to New Japan in the late 80s and his ascension to the head booker of the company the type of match known not-so-affectionately as "Lariat Puroresu" became the norm. These matches regularly featured repeated hits with a wrestler's signature striking move while the opponent attempted to endure them to show his "fighting spirit." It was not uncommon to see Riki Choshu use 6 or 7 lariats in one match to finish off an opponent, and his disciples like Kensuke Sasaki and Manabu Nakanishi followed suit. Choshu's hand-picked successor Shinya Hashimoto represented "Strong Style" perfectly during his years on top of New Japan in the 1990s. Hashimoto's offense was largely based around hard kicks and chops along with his signature DDTs, but he was able to project an aura of strength and power throughout his IWGP title reigns that had audiences coming to see him and the New Japan product in record numbers. Two matches that represent Strong Style in the 1990s are the 1991 and 1995 G1 Climax finals, the first match being the breakout performance by young superstars Masahiro Chono and Keiji Mutoh, and the second featuring Shinya Hashimoto relinquish his reign as "ace" of New Japan Pro Wrestling to Keiji Mutoh. My personal pick for a match that truly encapsulates "strong style" is when former top star Riki Choshu faced then-current ace Shinya Hashimoto in the 1996 G1 Climax.
There is some confusion on the internet and in some circles about just what "strong style" is. Part of that confusion stems from its early usage by Dave Meltzer and others in the Wrestling Observer crowd. They often referred to what we would now call "worked-shoot" and submission style wrestling as "Strong Style," especially in reference to promotions like UWFi and Pancrase. Dave has since corrected himself and noted that it is generally just a referent to New Japan's style. American Independent wrestlers and announcers also refer to many of their matches as "American Strong Style." To US Indy guys "Strong Style" = "Very Stiff" and features many head-dropping maneuvers more accurately associated with the All Japan style of wrestling, but such attention to detail can't be expected from people who are using "buzzwords" to cash-in on the niche of pro wrestling smart marks who follow the Japanese scene.
KING'S ROAD
King's Road is also called "Oudou" and it is the type of wrestling envisioned by All Japan's founder Giant Baba. Like "Strong Style" there were still hard strikes and stiffness, but by the mid-90s the matches were built differently with emphasis on a feeling out portion, a middle body working portion, and a finishing run. King's Road stressed stamina rather than mixed martial arts techniques.
You can basically say that King's Road is a logical progression from the US '70s style of wrestling from a build standpoint, but with the ante upped in the big move department, whereas Strong Style is a combination of traditional wrestling with the martial arts. Due to the heavy emphasis on top foreign talent from the NWA, King's Road tended to reflect the style of the NWA World Champions of the 70s, who focused on building a match and struggling for moves moreso than Strong Style, which features more back and forth action with quick transitions. With notable exceptions, this leads New Japan's matches to tell simple but strong stories, whereas All Japan's matches tend to try and delve a bit deeper.
King's Road was rooted in All Japan's direction under Giant Baba and through Jumbo Tsuruta, who worked a traditional pro wrestling style with some of the best gaijin (foreigners, literally translates to "outside people") of the era in the 1970s. Whereas Inoki looked to redefine pro wrestling as a style, Baba was content to hone in on the storytelling aspects of matches, using his extensive NWA connections and friendships to bring over the top American wrestlers like Harley Race, Jack Brisco, the Funk brothers, and Ric Flair to battle him and Jumbo. Prime examples of All Japan's style in the 1970s are the NWA World Title match between champion Terry Funk and young challenger Jumbo Tsuruta from 6/11/76 and an excellently structured match between Giant Baba and Billy Robinson for the PWF Heavyweight Title on 7/24/76.
By the early 80s many New Japan fans began to criticize Baba and All Japan for the slower and more methodical pace of their matches, but then King's Road was given a kick in the ass by Riki Choshu and his invading army in 1984. Ishigundan are responsible for significantly speeding up the pace of All Japan matches and incorporating quick tags and rapid-fire multiple-team moves, as well as shifting All Japan's booking focus from the old native vs. gaijin format to the more lucrative native vs. native programs. Comparing great All Japan tag team matches from earlier in the decade, such as the Funk Brothers vs. Bruiser Brody/Jimmy Snuka from the 1981 Tag League, to the main tag team feud of the mid-80s, Jumbo/Tenryu vs. Choshu/Yatsu, you can see the difference in pacing and moves.
With Riki Choshu gone, Genichiro Tenryu petitioned Baba to break away from his babyface team with Tsuruta and start his own heel group. Upon forming the group "Revolution" Tenryu became the most popular wrestler in All Japan, keeping the pacing and swagger from Choshu's group and incorporating harder strikes and hits like All Japan's top gaijin Stan Hansen. Tenryu was popular, but it took Jumbo Tsuruta's guidance and character to take what Tenryu and Choshu were doing and blend it with what All Japan was doing since its inception.
Jumbo Tsuruta took the traditional 70s style past the limit as he carried Genichiro Tenryu through the singles feud of the 80s in the absence of Choshu, creating the blueprint match that Misawa, Kawada, Kobashi, and Taue (often referred to as the Four Corners or Four Lords of Heaven) would follow and improve upon in the 90s. This blueprint involved a hot opening segment followed by a slow build to the bigger moves, constant teases of finishers and signature moves, playing off of previous matches and finishes, and telling a story within the context of a match based on the wrestlers' history with each other and their place in the promotion.
Tsuruta and Tenryu used the fast pace and adrenaline spurts from the Choshu-era matches and plug them into that formula to keep the matches moving in an age where the audience might not be receptive to two wrestlers working around a headlock or a headscissor for 7 minutes before moving on to the next hold to tell a story. All Japan was able to make that successful shift from using technical matwork to big moves to establish the roles the wrestlers were playing and the story of the match. Tsuruta's feud with Tenryu, culminating in their Triple Crown Title match from 6/5/89, established the formula that he would later build on by feuding with the younger generation of Misawa, Kawada, and Kobashi in the early 1990s.
Misawa and company took Jumbo's and Baba's developed style to the next level by incorporating more dangerous moves and complicated striking sequences, along with the use of adrenaline, or "fighting spirit," attempting to fight through the pain of moves to get in one last hit. With the unfortunate absence of Jumbo Tsuruta, the Four Lords rose to the occasion in the early to mid 90s and All Japan featured the smartest wrestling in the world, matches that were all tied together as one huge story that spanned years, and unraveled more and more with each match. Many people still herald Misawa and Kawada's Triple Crown Title match from June 3, 1994 as the greatest match of all time. To me, a quintessential "Kings Road" match was the last match in the style to truly live up to its full potential, the Finals of the 1996 World's Strongest Tag League.
As time went on (the late 90s), the All Japan style began to focus more and more on those "fighting spirit" segments and the big bumps that would lead to them, desensitizing their fans to the bigger moves and creating a "top this" environment in their big matches that the undercard couldn't match and the main eventers couldn't possibly keep up. The Kings Road of Baba, Tsuruta, Misawa, and Kawada was nearing its end. A new "Road" was constructed, but it lacked the depth and storytelling abilities of its predecessor; it was a shell. The top wrestlers still put out contests that nobody else could match, but building more on the spots and bumps took the focus off of the fundamental 70s style build that all of the best All Japan matches had at their heart. The "Head Drop Era" represented a regression in psychology and build, and thus a break with its foundation in US 70s style where the moves and holds were secondary to the story being told. Probably the last great example of King's Road was Kawada putting on an amazing performance in a Triple Crown match against a very broken down Kenta Kobashi on 6/12/98.
Once Misawa and friends left All Japan to form Pro Wrestling NOAH, the promotion began to look more like New Japan stylistically. The big matches after the split (Kawada vs. Fuchi, Kawada vs. Tenryu, Tenryu vs. Kojima) clearly had a "Strong Style" flavor to them with brutal strikes and big moves, but with little struggle to get them off. Mutoh entering the promotion exacerbated that effect, and now All Japan's style is essentially Mutoh's style with a sports entertainment bend and a few signature All Japan spots (like attacks off the ring apron and learned reversals) peppered in. Pro Wrestling NOAH's style is still essentially what All Japan was before the split, but with more Jr. heavyweight action thanks to the rise of Marufuji and KENTA, and a bigger focus on many strike exchanges as NOAH's main patriarchs, Misawa and Kobashi, can no longer wrestle at the pace they once could. I personally think NOAH is at its most entertaining when the matches and booking are refreshingly character-driven, such as when Masao Inoue challenged Jun Akiyama for the GHC Heavyweight Title on 4/23/06.
CONCLUSION
Don't necessarily let my focus on the 1990s and before discourage you from seeking out current matches from Japanese promotions, as there is still a thriving community of fans that greatly enjoys matches from New Japan, NOAH, and All Japan. I do, however, advise you to also look back to earlier years, as there is a wealth of great matches and great stories that have come from previous decades. I've offered only a few suggestions here.