Some models devices get the specialized Apple TV+ app (no Store, no Library, no channels), instead of the full Apple TV app (with Store, Library, and channels). Which one is available to you is based on the exact model TV or streaming device — not user choice. I don’t think devices can have both. Get the Apple TV app or Apple TV+ app on your smart TV or streaming device - Apple Support

If your smart TV gets the Apple TV+ app, and you would want to use the full Apple TV app instead, then you could get an external HDMI streaming device that supports the full Apple TV app. That can be an Apple TV box, Roku, Fire TV, PlayStation (4, 5), Xbox (One, One S, X, S), ‘Chromecast with Google TV’-dongle, or Nvidia Shield TV.