I’ll try to explain to the best of my ability, from having used both and figuring things out.
On Atproto, the federation is very much more on the backend, where the Personal Data Servers are interlinked and people access the protocol through bsky.app or some other app they wish to use. They have started rolling out the infrastructure to allow federation between different PDSs and have started moving user data to them. They’ve made for a more predictable, consistent federated experience (which has been a criticism of the ActivityPub’s fediverse), and allowed for a more resilient infrastructure, but unfortunately it’s limited to what Bluesky wants which is just microblogging while ActivityPub is more flexible (see: Mastodon, Lemmy, Funkwhale, PeerTube, Wordpress, etc.) but has the cultural issue of people treating their instance like their own personal forum and not a critical part of the fediverse’s infrastructure.