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.
Apple TV Channels can only be viewed within Apple TV; you cannot watch an Apple TV Channel service’s content on any non-Apple TV device, app, or the web. However, if you subscribe to the same service within that service’s app or through a cable TV provider, you can watch that service’s content on other devices and apps and, if you use the service’s app on Apple TV or iOS/iPadOS, its content will show up in Apple TV as though you were subscribed to the service’s Apple TV Channel (but it will play the content in the app, not within Apple TV).
Apple TV+ is a subscription streaming service from Apple that functions like an Apple TV Channel but is not an Apple TV Channel.
Other than that, though, Apple TV is relatively straightforward.