To be able to watch much of the same TV channels as you were used to with your local cable provider, you will need to subscribe with a streaming provider that carries those channels.
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These have apps for the Apple TV set-top box, for iPhone, and iPad. You may be able to view some of these in a browser on a computer.
The subscription to Apple TV+ is different. This subscription gives access to Apple Original shows, not other channels.
Inside the Apple TV app, you may also subscribe to other VOD premium channels, such as: Acorn TV, A&E Crime Central, BET+, Britbox, CBS All Access, Cinemax, Comedy Central Now, Epix, Lifetime Movie Club, MTV Hits, Mubi, Showtime, Starz.