I think that’s a part of it but doesn’t state it fully.

AT doesn’t just give consistency, but a shared data model across apps. So apps can reference and render content from other apps. It’s really kind of like a web of typed JSON. Different apps are lenses through which you can see the same network. Anyone can build new experiences on top of old data. There’s nothing remotely equivalent in AP.

AP couples data to apps. In AT, it’s more like there’s one global database with entire world’s data that every app can query.

I don’t understand why the discussion always bumps into Relays. Running a Relay if you want to is cheap-ish ($30/mo) these days. There’s multiple existing ones (Bluesky or community) you can use for free. And many apps don’t use one at all and rely on community indexes like Constellation (https://constellation.microcosm.blue/). Some don’t even run their own server or database.