Technical problems give way to philosophical differences but the over-arching problem is that the people behind ATProto really want to make a social media ecosystem that attracts lots of average people who will refuse to understand that the solution you're giving them can't do things Twitter could do back before Musk bought it. People get angry enough at Bluesky not having an edit button, and it's at least possible to talk about how editing can be abused.
An "AppView" is the API server that most clients connect to that aggregates data from the network and serves it in a more useful way. mu.social still uses bluesky's AppView (api.bsky.app).
The name is confusing. I thought clients were appviews myself for a while.
I kind of started calling them all “apps” with true appviews being “independent apps”. I think sometimes it makes sense of think of this as an implementation detail. For example, Mu could actually switch to its own database if they do a bunch of technical work in the future. From the users’ perspective, it wouldn’t be noticeable.