It appears to be in the eye of the beholder. Somebody living by the Amazon or the Nile might consider the Potomac to be a creek.
According to the US government's educational site, the terms are interchangeable.
How big does a waterway have to be before it's called a river?
During the late summer I can jump across the North Fork of the American River in CA. Is is somewhat smaller than the Mississippi, but still called a river.