Precisely that yes, they all use activity pub to communicate. Firefish/Calckey was forked from Misskey which was/is? huge in Japan and created before mastodon. It’s got extra features missing in Mastodon and basically it’s personal preference on which to use. There are other options out there too Pleroma, Akkoma and more.

Firefish was created to enhance on Misskey, anglosise (is that a word) it and enhance it’s security and usability.

One downside is the lack of apps for mobile on Firefish, but they are creating their own and the PWA works rather nicely.