There are four, possibly five distinct products called "Apple TV", including hardware, software, and a service.
(Apple) TV app : program that lets you access video media sold by Apple and other streaming services that let Apple index their media (which is all except Netflix)
Apple TV+ : subscription service to access video media produced by Apple
While not the most clear situation, it’s not too bad, in my opinion.
Apple sells media that others produce, but they also sell subscription only access to media that they themselves produce.
So movies and tv shows that you “buy” (really, rent for as long as Apple allows you to access it) can be accessed via the TV app. Basically, the stuff where Comcast or Disney or Sony or Warner Bros gets paid 70% and Apple gets a 30% commission.
But for things Apple directly produces (or buys and then re-sells), they require customers to pay an ongoing fee for Apple TV+.
Also, LeoPanthera is right that the TV app can also be your library for your own files that you import, and then you can synchronize that to your phone or iPad’s tv app.