Pass-through
The partner passes along the cost of the service to their customers, sometimes taking a cut of the revenue as a fee.
Picking-up
The partner pays for the cost of the service on behalf of their customers. This eats into margin so they will want to negotiate the lowest possible price. The upshot is they are the customer and be more invested in the partnership.
Wholesale
The partner packages the product, collects payment, and you bill for usage. The partner gets complete control over pricing so they can tailor it to their customers.