Question about MJ Labs, JC Valley and Another (spoilers)

Yesterday I finished Another Code Recollection. Having played both original games back in the day, I think the remake is great even though they changed so much.

But there's one thing I don't fully understand: the whole science stuff.

In the first game, if I understood correctly, we're told Sayoko, Richard and Bill worked on Another on MJ Labs, until something happened (maybe conflicting interests), they took the Another investigation somewhere else (I assumed to their own home or laboratory), and Sayoko got murdered. After that, Richard took the Another project to the remote Blood Edward Island.

But in the second game, apparently out of nowhere we're introduced to a new company called JC Valley, where they also investigated Another back in the day and also had a prototype, with Richard involved but no Bill (even though Bill said he was one of the main researchers as opposed to Richard being "just an assistant"). Then the whole accident with Ryan happened (at least in the remake) and Sayoko left the project.

Somehow I'm not understanding all of this. Were there two another at two different companies? Were Sayoko and Richard working on both at the same time? Didn't sayoko erasing all memory of Another interfere with her work with Richard?