Apple TV, Apple TV app & Apple TV+
The Apple TV is a physical device that you connect to your TV via an HDMI cable and you install apps on it, such as Disney+, Netflix, HBO Max, Fox Sports, etc. It also has the Apple TV app installed on it.
The TV app is an aggregator app that pulls in content from various providers, like those mentioned above, and is a one-stop-shop for keeping up with what you are watching and discovering new content to enjoy. Through the TV app you can also subscribe to various Channels such Paramount+, Showtime, AMC+ and Apple TV+. There is no subscription to use the TV app.
Apple TV+ requires a subscription to view the majority of the content and it is billed through your iTunes account. A subscription to TV+ does NOT give you access to everything you can find in the TV app; only to the TV+ content.
There are Channels in the TV app for Up Faith & Family, Acorn and Britbox. None of these Channels include a live stream, they are all Video On Demand. They all require a subscription to the Channel. You can see this information in the TV app.