So, using your Apple TV and the Apple TV app, you could possibly watch all the channels in your cable/satellite package without renting a receiver from the cable/satellite company, right? If that's possible, I don't see why anyone would want to do that. The Apple TV doesn't have all the functionality of a DVR receiver.
So, I use my Apple TV to watch any MLB game I want, and I use it to mirror things from my Mac or iPhone. I'll be canceling the Apple TV+ before the free trial ends. There's just nothing there that interests me enough to pay 5 bucks a month for.
As for the naming, they could have gone with Apple iTV for something, either the device or the app. But, the i next to the T doesn't read very well. It's like MLB.tv and The MLB Network for baseball. The former is the app for streaming games, and t he latter the channel on cable or satellite.