Cael is right. Each game, manga, animes, certain dramas, etc. have nothing to do with each other. So, Platinum Stars (just like Idolm@ster 1 and One for All) takes place in a different continuity than Idolm@ster 2 where there is no Ryuguu Komachi.
There are a few exceptions like the anime and Movie taking place in the same universe.
In most iteration of 765pro, they start off as rookies idols who work their way up to top idol. But, the setup and perspective in each is slightly altered.
The foundation in all of the iterations is usually the same with the characters and their general story, personality, and character interactions. However, each iteration usually has a different producer, different rivals, slightly altered idol story, slightly different character interactions, etc.
It's basically the story of 765pro that gets retold.
Second vision (one way to put it) was mainly a 765pro reset (adding new members, age changes, hair styles, etc). So, it set a new foundation for future iterations.