This question does get asked a lot, as someone else pointed out. But even if you go back to when it was asked a couple of years ago the consensus has always been lemmings.
We really need to get a search function so this post can stop being asked 1x daily by some new refugee.
Don't get me wrong, I'm glad y'all are here and it moves a lot faster than 2y ago, but every day with this question, and no consensus has been reached. We should all just stop "asking" and let time tell us what we call ourselves, some word will win eventually.
Before any of the iOS apps were worth a damn, I decided to try and figure out how to make an app myself. I was going to call it Ace, and hope that at least someone knew why.
I didn't get very far though, because I've literally never made an app before.
Lemmies are the Instances themselves, actually. Lemmy.world, lemmy.ml, beehaw.com are all Lemmies/Instances/Servers. The terms are used interchangeably, with most calling them Instances.