Stripe is a Payment Facilitator, and they pioneered the modern PayFac model. That’s one of the reasons that the word Stripe appears on your credit card statement when you pay someone that is using Stripe. Additionally it means they front the risk of accepting payments on your behalf. They are also a payment processor. Those aren’t exclusive operating models, at least in the US.

https://stripe.com/payment-facilitation https://stripe.com/guides/payfacs