Payment provider
A payment provider is the service that captures money from a customer's card, bank account or other payment method on behalf of a business.
Also called psp, payment service provider.
It handles the movement of funds. It does not decide what the customer owes, which is the billing system's job, and confusing the two is how businesses end up with pricing logic trapped inside a payments integration.
Most businesses of any size use more than one, by region or by payment method, which makes keeping billing independent of any single provider a practical requirement rather than a principle.