It's the difference between Hoovers and Vaccum Cleaners; the iPod is the market leader, and as such the name is often associated as a name for any such device.
though tomd's is plain and simple i will go into a little more detail.
iPods are made by apple, who are also responsible for the macintosh operating system. For this reason they are more compatible with Mac.
Now, Music files come in many file types. Both operating systems have there own types. For Windows there is: WMA, WAV. For mac there is: AAC, AIFF, MPeG-3. The latter will only play on ipod's. the first ones will only play on mp3 players.
Mp3 is an old format had has been superceded by Mp4 which offers better sound quality and smaller file sizes. The iPod is designed to play Mp4 (but will still play mp3s). Though it is an Apple product, it is fully compatible with Windows, and is no more or no less compatible with any operating system. Apple runs the iTunes store which is by far the largest legal download sight, and the iPod should work seemlessly with iTunes software which is a free download (the software is included when you buy an iPod).
An new version of the iPod is imminent.
I agree with Gromit's answer; charlie_h is incorrect in what they say.
Note though that it may be a bad idea to buy songs from the iTunes Music Store, as they're encrypted with DRM which stops the music from working on anything other than iPods.
fo3nix, the origional question was what is the difference between Mp3 players and iPods. Not Mp3 files and Mp4 Files. Therefore that renders your comments obsolete.