iPod is just Apple's branding for their MP3 players (although now they're more accurately just portable media players, since they also play video as well as audio).
As for iPods vs other media players...really it just comes down to storage capacity with an ultraportable form factor and good sound quality (iPods do tend to have higher maximum storage capacities than most of their other competitors...the iPod classic is availiable up to a whopping 160GB, while the only other one with that kind of capacity, the Archos 605, is notably bigger in terms of physical dimensions and more expensive, although for video playback I would recommend it over the iPod).
Then you have the iPhone and iPod Touch which are more like a smartphone and PDA respectively, rather than a dedicated media player.
Really though...if you don't need the large capacity and don't care about Apple's user interface, you're better of with going with any notably cheaper player rather than the iPod. In the low capacity market, iPods are typically notably more expensive than the other products available.