Hi Tim, well technically an avatar is just a small picture to represent you, it can be a number of types of file including a .gif or .jpg and obviously doesn't have to be animated.
An animation is just made up of several smaller pics as Linda mentions and then these are manipulated within software and then saved as an animated gif. Each frame would initially be saved with it's own name (beers1.gif, beers2.gif) but once added to the animation only the final animation has the file name, not the individual frames.
Animations can only be saved as a .gif as opposed to a .jpg unless of course it is made using flash or a similar tool. Flash animations are a much better quality but also produce a much larger file size.