The number of devices and services using the Apple TV name is numerous and a little confusing. I’ll try to explain.
There’s the Apple TV app- or more commonly just called “the TV app”. This app is free and built in on most of Apples devices. Best way to think of this app is as a big directory for TV content. You can search or anything inside and it’ll point you to the best place to view it. Whether that be iTunes and you can choose to buy or rent, through a streaming service like Hulu, or if it’s exclusive to a service like HBO. It’ll tell you.
Then there’s Apple TV+- this is a new subscription service that lives inside the TV app and gives you access to Apple owned and original programming. I personally like the list on Wikipedia (https://en.m.wikipedia.org/wiki/List_of_original_programs_distributed_by_Apple_TV%2B) so you can see what all is exactly on Apple TV+.