Apple TV, Apple TV, Apple TV, and Apple TV+
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 is an app or built-in feature of other devices, like smart TVs and streaming set-top boxes, but when Apple TV is running on a third party device, it does not show content from other installed apps on that device.
Apple TV Channels is a feature on all Apple TV apps that lets you subscribe to external services like HBO and Showtime, which then display content within Apple TV. When Apple TV is on Apple TV or iOS/iPadOS, though, most Apple TV Channel services also have their own app. If you are logged into the app, the service’s content already shows up in Apple TV.
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.
Apple TV+ content can also be viewed in a web browser at tv.apple.com; no other Apple TV apps, devices, or features can be used in a web browser.
Apple TV content that supports special features like 4K HDR, Dolby Vision, or Dolby Atmos can be watched with those features only through Apple TV on Apple TV or Apple TV on certain unspecified Samsung TVs. It is not clear if Apple TV streams HDR content to iOS devices, but it might. There is no way to tell which device supports which set of features or which level of streaming quality – and no way to know which features are active when playing content.
Other than that, though, Apple TV is relatively straightforward.