AVI is a type of video file; as are MPEG, DiVX, etc. An AVI player is nothing special, it's just a video player that has the capibility of reading and playing AVI files. Take for instance Windows Media Player. With the proper Codecs installed, it can play any of the above formats with no problems. So can Quick Time, DiVX Player, Real ONE Player, and so on.
If you don't know, a Codec is basically a few sets of files that makes your video player capable of reading different file formats, and it gives it settings on how to read those files (for performance and whatnot.)