FedEx is a company that has no affiliation with the U.S. Post Office or any government agency, despite having the word "federal" in its name.
FedEx was the groundbreaker in the late 1970's as the premier courier of overnight letters not delivered by the U.S. Post Office. They still rank number one in that type of service delivery, however, they do charge a higher rate for that service.
UPS has taken over 70% of package delivery from the U.S. Post Office. They are the largest private delivery service in the world. As they have steadily increased their hold on package deliveries, they have recently added overnight letter delivery service.
Even though UPS is not as expensive an option as FedEx, they do have a good service delivery record, and have a variety of delivery options to choose from including next-day air, ground service, and international.
U.S.P.S. has been our national delivery service since the days of our founding fathers, including our first Postmaster General, Benjamin Franklin. To this day the U.S.P.S. still controls the delivery of everyday postal letters and standard mail delivery within the United States
The U.S. Post Office was the only player in the delivery of overnight letters until the late twentieth century when Congress permitted private companies to offer these services. Comparatively the U.S.P.S. offers low cost overnight delivery options as well.