No - it’s more like email. ActivityPub is the protocol (I think loosely equivalent to sftp or http). Each fediverse “app” (mastodon, lemmy, pixelfed, etc) is a layer of API built on top of ActivityPub. I’m not a web developer so I don’t know the exact analogue here, but it’s maybe like different flavors of webmail, or like different message boards that are email based.

Basically, every “instance” is running the lemmy application. Different lemmy instances communicate with each other using the lemmy API and the ActivityPub protocol. In principle, a lemmy instance could communicate with a mastodon instance because they use ActivityPub under the hood, but someone would need to translate the API - mastodon has no concept of upvotes or downvotes for example, and lemmy doesn’t seem to know what a boost is (boosting, formerly “retooting” is analogous to a retweet on Twitter).