Apple TV is a hardware device.
Apple TV is an app on Apple TV that curates content you can buy from Apple and also content you can stream through other installed apps (but not all apps, and there is no way to tell which ones).
Apple TV is an app on iOS/iPadOS devices that operates similarly to Apple TV on Apple TV. Apple TV on iOS/iPadOS syncs playback and watch history with Apple TV on Apple TV, but only if the iOS/iPadOS device has the same apps installed as the Apple TV – and not all apps are available on all platforms. Apple TV is also an app on macOS, but it does not show content that can only be streamed from external apps on an Apple TV or iOS/iPadOS device.
This stuff is confusing enough without this kind of crap. How can the average, non-techy user figure this out?