Both generally refer to the same 'family' of pigeon breeds. Some do flips in the air (most common breed who roll in the air, are Birmingham rollers), and others do flips on the ground (such as parlor tumblers. Some call them parlor rollers as well). The names are often mixed up since some people just prefer to call them one or the other. BUT regardless of what people call them, the breeds do have a set name. There are many breeds of each, but typically you'll find most the rollers still roll, but not all the tumbler breeds still do. In fact there are quite a few breeds of tumblers who are mostly for show purposes only.