Check sub.rehab for a list. A few of them are official (the old Reddit mods are the new mods of those communities), while some are spin-offs (comms created for the same purpose as the original).
The site above is listing alts elsewhere, too - raddle.me, kbin.social, even Discord. Note that you can often access Kbin content from Lemmy and vice versa.
The right term is "community". Personally I shorten it to "comm", have seen other people doing it but it isn't that common. I'd advise you to avoid "sub", as plenty people call it out as "Reddit thing".
Also, please keep in mind that this community is about Reddit, not Lemmy. You'll probably get better answers in a comm about Lemmy itself, such as [email protected]