Hi Hiroshi,
I asked for (and got) a lot of information about Madhyamika vs. Yogacara. You can read it here:
http://www.lioncity.net/buddhism/index.php?showtopic=4992
(On that board I use the username Skywalker.)
Regarding the relationship between those two schools and Buddhism in Japan, there seems to be little connection.
Buddhism in Japan falls mostly into these groups:
1.
Shingon and Tendai, both imports from China
2. Zen, also an import from China
3. Jodo, which was started in Japan, because there were things in Buddhism that Jodo's founder did not like
4. Nichiren, which was started in Japan, because there were things in Buddhism that Nichiren's founder also did not like
5. There were many new religions started in Japan in the 20th century. Some of them were mere cults, usually centered around one charismatic person. For example, you may have heard of Aum Shin Ri Kyo, whose members killed people on a Tokyo subway a few years back.
~~~
Buddhism in Japan has evolved into its own forms. They usually do not get into discussions about things like the difference between Madhyamika and Yogacara.