Nakamura was expelled from kyokushin, and there was a lot of bad will between him and Oyama (from Nakamura being tagged as Oyamas successor and heir-apparent) for a long time. The reason was officialy that Nakamura opened his own (non-kyokushin) dojos, during his time as the head kyokushin representative in the USA.
Inofficialy, Nakamura apparently lost out in the political backstabbing game that was kyokushin internal powergame/politics back then.
From what Ive seen Nakamuras style seido juku is more or less identical with kyokushin in formal technique and kata, but Ive heard that they dont do full contact knockdown rule sparring anymore, but goes for semicontact point sparring. Also Nakamura has starded focusing on his own brand on zen and philosophy, and include it in the trainin, and Im not sure I like that.
The main reason seidokaikan of Ichii changed its name outside of japan, was that it kept beeing confused with the seido juku of Nakamura in the states-
Btw, I didnt know Nakamura had made any tapes. Could you give me a title or two, and possibly a link??