There is a difference, they are separate services that are not exchangeable. They have different perks, and different terms and conditions. If you mix them up, then you may end up with two subscriptions for the same content, even in case that both are payed through Apple.
Apple TV Channel subscriptions are accessible exclusively through the Apple TV app.
Apple TV Channel subscriptions allow family sharing.
Apple TV Channel subscriptions allow downloads for offline use (iPhone, iPad, or iPod touch).
Apple TV Channel subscriptions should have about the same content.
Apple TV Channel subscriptions have one price per service, without tiered options that the original content provider might have.
Apple TV Channel subscriptions may have a different duration of the trial period.
You can’t take your watch history with you, if you switch.
Apple TV Channels FAQ: Services, pricing, availability, and everything else you need to know - Macworld
Subscribe to Apple TV channels in the Apple TV app - Apple Support