If you subscribed to Disney+ with Disney directly, then you will have a Disney+ account with which to sign in to their app.
If you subscribed to Disney+ through the Disney+ app on an Apple device, then you subscribe with payment through Apple (linked to your personal Apple ID), but also confined to your Apple devices.
These types of subscriptions are generally not exchangeable. These types can exist side-by-side.
The price of Disney+ is not 9.99 when I look it up?
Disney+ pricing - Disney+ Help Center
In-app purchases - Disney+ app - App Store preview - Apple
Apple TV+ can be 9.99, but does not include any of Disney+.
Disney movies and TV shows on the iTunes Store are separate from any subscription, as buy or rent purchase.