Medical residency is acquired after graduation and internship, while fellowship is done after residency. Residency is additional training on an individual's chosen field of specialty, while fellowship is a further in-depth training within his field. The government funds both, and those who only went to practice medicine can only get a residency. However, those who want to enter academic medicine must have a fellowship.
Those who want to work in small communities need a residency, and those who want to work in a more significant community or medical establishment would need a fellowship as well. The requirement for a fellowship depends mainly on the individual's field of specialization and the area where he wants to practice medicine.