Two different subscriptions
The seller's platform subscription is the monthly software plan they pay to Just My Site.
A buyer subscription is a recurring membership or recurring product the seller sells to customers.
These should never be described as the same system, even though both use payment providers behind the scenes.
Stripe recurring flow
If the active seller provider is Stripe and the product is recurring, checkout runs in subscription mode inside the seller's Stripe account.
The app stores local order and payment-attempt records and then uses those records to support access, delivery, and reporting.
Refunds, disputes, and subscription finance visibility remain primarily managed by the seller in Stripe.
PayPal recurring flow
If the active seller provider is PayPal and the product is recurring, the app ensures a seller-scoped PayPal catalog product and billing plan exist.
After buyer approval, the app syncs membership status into local membership and access records so the buyer can receive access in the platform.
The seller still manages the commercial and provider-side subscription relationship in PayPal.