A question I sometimes get from people who are not familiar with judo is: "Are there many types of judo or only one judo?" The short answer is there is only one judo.
The longer answer is that there is only one universally-recognized form of judo, that which is defined by the International Judo Federation (IJF). Karate, taekwondo and even boxing all have many competing governing bodies. But in judo, we have only one: the IJF. As a result, there is uniformity in terms of the rules of the game as well as the weight categories and so on.
This doesn't mean there aren't different styles of play. A Georgian player for example fights very differently from a Japanese player. But both of them train and contest under the same rules. In terms of influence though, there is no denying Japanese judo prevails in many parts of the world.
When judo players say "Japanese judo" they are usually referring to a few general charactertistics. For example, a lot of Japanese players are left-handed. This is by design because being a left-handed player does give you a slight advantage. Japanese coaches tend to encourage their players to adopt a left-handed stance and take a traditional sleeve-collar grip. And from there, they will do beautiful, classical judo.
Japanese players don't just aim to win but to do so with ippon. Japan's greatest champions like Yasuhiro Yamashita, Ryoko Tani, Toshihiko Koga and Kosei Inoue are all ippon judo players who believe how you win a match is also very important. This is the Japanese ethos.
American judo is very Japan-influenced because many of the early judo clubs were founded by Japanese immigrants. Many of its top players also trained in Japan for extended periods of time. World Champion Mike Swain actually lived in Japan for years. He happens to be left-handed and prefers a traditional sleeve-lapel grip. His throwing techniques are as classical as it gets. Tai-otoshi and ouchi-gari are his favorites. He is even married to a Brazilian-Japanese woman, Tania Ishii, daughter of Chiaki Ishii, Brazil's first Olympic medalist (bronze in 1972).
Japanese judo has also had a great influence in Brazil, where many of its pioneers were from Japan. Even today many of its top players have Japanese-sounding names like Chibana, Takabatake and Kitadai. Brazilian judokas are known for doing beautiful, classical judo just like the Japanese.
The UK is another country that has a strong Japanese judo background. The Budokwai, Europe's oldest judo club, was founded by Gunji Koizumi in 1918. He had trained in ju-jitsu and originally taught ju-jitsu at the Budokwai, not judo. In 1920, Jigoro Kano, the founder of judo, visited the Budokwai on his way to the Olympic Games in Antwerp. After some discussion, Koizumi agreed to switch to judo, and Kano awarded him a second dan (degree) black belt in judo.
It's interesting to note that many of Britain's most successful judokas had very Japanese-style judo. In the 1980 Moscow Olympics, Japan's great champion Yasuhiro Yamashita (who was denied a chance to compete there due to the US-led boycott) declared that the best player of those Games was Angelo Parisi, who despite being a heavyweight, had beautiful, flowing judo like the Japanese. In Moscow, Parisi had won the +95kg gold and Open weight silver for France (where he had moved to after marrying a French girl) but his formative years were spent at the Budokwai in London.
World Champion Neil Adams's juji-gatame was highly original and in a sense, very unorthodox but his tachi-waza was absolutely classical. He preferred a standard sleeve-lapel grip and all his main techniques — tai-otoshi, uchimata, kouchi-gari, yoko-tomoe-nage, drop seoi-nage — were done off that classical grip. He too was a product of the Budokwai in London.
Today's French style of judo is often associated with high-gripping and oftentimes, (especially among the male players) a mauling style of judo reminscent of the Georgians.
World Champion Stephane Traineau, for example, liked to grab the belt when doing his techniques. So did his teammate, Olympic silver medalist, Pascal Tayot. Djamel Bouras famously defeated Koga in the Atlanta Olympics using this mauling style of judo where he constantly grabbed the belt. And if you look at the judo of Olympic silver medalist Larbi Benbaoudaud, you'll find it doesn't remotely resemble Japanese judo. All this is a product of Eastern European judo influence.
But French judo had its origins with a Japanese figure as well. If Gunji Koizumi was the father of British judo, the father of French judo has to be Mikinosuke Kawaishi (who was a good friend of Koizumi).
Kawaishi lived in London from 1928 to 1931. He briefly taught judo at Oxford University in 1931 but later that year, returned to Japan where he was awarded a 3rd dan (degree) from Jigoro Kano. In 1935, he moved to France and spearheaded the development of judo there.
While Koizumi in London basically adopted the Kodokan way of teaching judo, Kawaishi felt the traditional Japanese approach was not suitable for French people and came up with what came to be known as the "Kawaishi Method".
One of the first things he did was to rename the techniques using a numerical system. He figured this would be easier for French people to remember. So, intead of having to memorize the term osoto-gari, they learned "first leg movement" and instead of kesa-gatame, they learned "first hold-down". This seems rather odd but at the time this simplistic approach worked. Judo's popularity spread far and wide.
Today, judo is popular in France in a way that is hard for non-French people to imagine. It has penetrated society more deeply there than in any other country. You might be surprised to learn there are more registered judo players in France today than there are in Japan.
Judo is to France what badminton is to Malaysia. You can play badminton wherever you are in Malaysia. In France, you can do the same for judo. Every city, every town and every villlage in France has its own judo club.
Speaking of Malaysia, what about the judo here? Does it have a Japanese influence? Almost completely. Every judo club in Malaysia (with the sole exception of KL Judo Centre) teaches judo based on the Japanese way.
Beginners spend an inordinate amount of time learning ukemi (breakfalls), often for months on end. Uchikomi is prioritized over almost everything else. Nagekomi is done on tatami rather than crash pads. Randori is forbidden for beginners.
Some clubs take it to the extreme and don't even allow their players to drink water in between randoris just because traditionally, the Japanese did not do this. (Today's top Japanese judokas drink water though).
We are all products of our experiences and upbringing. Judo coaches here were either trained in Japan or were trained by Malaysia-based Japanese senseis. It's natural that they would run their training the Japanese way.
It so happens my training was at places like LA Judo Training Centre in the USA, Camberley Judo Club in the UK and Russelsheim Olympic Training Centre in Germany, where judo is treated not as a traditional martial art but as a modern Olympic sport. I never trained in a traditional dojo setting. That's why I call for lots of water breaks, encourage the use of crash pads and play music during training.