As someone who keeps rats as pets, let me tell you this - rats have larger ears, larger eyes, etc. and a much more scaley, long tail even if they're tiny. They come in a variety of colors, as Seven-Thirty said, and generally they are less skittish than mice - HOWEVER if you bought specifically branded feeder rats, they might be just as if not more skittish.

http://www.ratbehavior.org/RatsMice.htm

This page has pretty good pictures if you scroll down some to compare the differences of a juvenile rat and a fully grown mouse.