These days when people say "MP3" they often mean a portable player that can play MP3 audio files. The iPod is one of these, but just about all portable players (except for some Sony models) can do that.
Most non-iPod players also play WMA (Windows Media) files. iPod instead supports AAC. This is the main difference (especially when either file type carries copy protection) that brings in the compatibility issues.
In general, MP3 files are MP3 files, though, and will play on just about anything. It only gets messy when you look at the commercial download services.
Warbrain said:
There's a big difference between an iPod and an MP3. They're two entirely different things. An iPod is a Digial Music Player (DAP) and an MP3 is an audio codec.
Historically. Generic audio players have been marketed as "MP3s" for some time now, and generic video players as "MP4s". Words change.