Apple made things a bit confusing with names, there's AppleTV and AppleTV+ (Apple TV Plus).
AppleTV is the hardware box.
AppleTV+ is the streaming service from apple. Similar to Netflix or Prime Video. A subscription is required to watch shows from them. If you don't have a subscription, it just prevents you from watching those particular shows.
There is also the TV app on the appleTV.
The TV app is where you access the programs from appleTV+
The TV app will also search most of the other streaming services, So you can search for a show or movie, and it will list all of the services it's available to watch, as well as the price to purchase or rent, or if it's included with a subscription to a particular service.
The TV app will also consolidate an "up next" list for most of the streaming services, So you have one place to look where you can see if new episodes of shows you've been watching have released, no matter if it's on Prime, Hulu, Disney+ or Max. When you select one of those shows, it will launch the appropriate app and play the file there, you must have a subscription to that service.
One notable exception to all that is Netflix, Global search will sometimes return items from Netflix, but they won't be added to the up next section.