Connect existing subscriptions to Apple TV Channels

No. Apple TV Channel subscriptions are different items. If you want to switch, then you have to get a new subscription and cancel the old subscription.

Subscribe to Apple TV channels in the Apple TV app - Apple Support

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 (perhaps with exception of live content if applicable).

Apple TV Channel subscriptions have a fixed 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.

Personally, I think it is more about getting new subscribers than converting subscribers.

Apple TV Channels FAQ: Services, pricing, availability, and everything else you need to know - Macworld

How Apple TV Channels prices compare to native apps like HBO Now, Showtime, and CBS All Access - Macworld

The new Apple TV app and Apple TV Channels: 9 things you need to know - Macworld

Are there any differences in the subscription types beyond this? Any limitations with getting the subscription tied to Apple TV app vs. the subscription directly through HBO?

Thanks for the rundown here. Helpful to understand.