Pleroma is a small Fediverse chat server that is increasingly compatible with Mastodon, because you basically need to be these days. Pleroma is favoured by Nazis for unfortunate historical reasons - one Nazi wrote a how-to on putting up a quick throwaway Pleroma instance, and now if you get a horrible chud in your Mastodon notifications guess what they'll be posting from.

Politically, the Pleroma devs are NOT NAZIS but they are most definitely the other ten guys at the table.

Soapbox is a fork of Pleroma by Alex Gleason, after he was kicked out for being so obnoxious that even the other ten guys at the table wouldn't put up with him. Gleason is a transphobic gay man who started TERF instance spinster.xyz, which federated with Gab. Gleason was working at Truth Social for a while and quit that to work at Nostr, which is Bluesky with bitcoins and more overt Nazis. Posting from Soapbox at all is likely to get people on Mastodon looking askance at you and causing their fediblock finger to twitch. Soapbox is extremely favoured by the Dark Fediverse of all the sites that were such shitheads that they get widely blocked.

Akkoma is another fork of Pleroma run by nice people. Gleason called Akkoma the "tr***y server" which I understand they were most amused by. Akkoma is the one of these to go for.

If you run Mastodon, run the Treehouse+Glitch patch set. It's where features that Website Boy has decried as unacceptable get popular before Website Boy suddenly decides they were a great idea all along. (Recent examples include quote-tooting and search that works.)

If Pleroma looks good, run Akkoma.

The third chat server is Misskey, and you want the Firefish fork (formerly Calckey) because Misskey is also run by transphobes, which led to Calckey declaring themselves a fork and not just a patchset and changing their name.

All of these are progressively approaching the Mastodon extensions to and interpretations of ActivityPub because that's where the action is.