USPS had (maybe still have) a partnership with FedEx for reselling FedEx's express courier services. USPS take the parcel and fee at their counters, and hand it to FedEx for delivery.

A supplier once used USPS to send a FedEx package to me using a guaranteed 2 day delivery. 2 days later -- no sign. I was able to obtain the tracking number, and it turned out that USPS had not gotten around to giving the package to FedEx yet. Only on the third (business) day did USPS give FedEx the guaranteed 2-day delivery parcel, which FedEx delivered next day.

KP