The Fediverse has been around for over 15 years now. In order for one app/server to talk to another, they need to support the same protocol. Mastodon and Lemmy (and Pixelfed and many others) use a protocol called ActivityPub. Since they both use it, you can actually reply to Lemmy comments using Mastodon.

Not all of the Fediverse uses ActivityPub though. For example, the original Fediverse apps like Identica and StatusNet used Activity Streams or OStatus instead. ActivityPub didn't exist yet.

AT Protocol is another protocol, created specifically for Bluesky, although there's no reason other apps couldn't use it, once Bluesky actually enable decentralization.

It does have some useful features that ActivityPub doesn't have, like identity portability - you can move a profile from one server to another without having to change username or refollow everyone. AT Protocol lets you use your own domain name as your username, even if you don't host your own instance. With Mastodon and Lemmy, your identity is tightly coupled to the instance you use (i.e. an account on Lemmy.world is always going to have @lemmy.world at the end), which makes it a pain to move to a different one.

The rest of the Fediverse runs off ActivityPub.