I want to watch a movie offered on my AppleTV app. Am I able to watch this on my TV, or only on my laptop?

• Select smart TVs support the full Apple TV app.
• Select other smart TVs support the Apple TV+ app, being just for the Apple TV+ service.
• The remaining TVs will have to use an external streaming device that supports the Apple TV app.

The difference the between the Apple TV app and Apple TV+ app is feature support, as detailed on: Get the Apple TV app or Apple TV+ app on your smart TV or streaming device - Apple Support.

Which one is available to you depends on the exact model smart TV, which seems to align with age and OS support.

Supported devices with the full Apple TV app will be able to stream purchased movies, through the Store tab and through the Library tab. Devices with the Apple TV+ app do not have this feature.

List of Apple TV(+) app-supported devices - Apple

All the ways to watch in the Apple TV(+) app - Apple Support