The Apple TV app Channels are not exchangeable with subscriptions and bundles from a TV provider. The Apple TV app Channels are a substitute for select premium channels individually, with Apple as its reseller and deliverer.
Apple TV Channels FAQ: Services, pricing, availability, and everything else you need to know - Macworld.com
Subscribe to Apple TV channels in the Apple TV app - Apple Support
To use the bundled services from your TV provider on the Apple TV box, you have to download the apps for these services. Maybe your TV provider has published their own app with all their services. (Checked: only for iPhone and iPad, not Apple TV.)
To use e.g. ABC, HBO Go and Showtime Anytime, get all of their respective apps. Each app will want you to sign in with your TV provider credentials, unless your TV provider supports Single Sign-on.