mimi-moomoo's rant is a little incorrect anyway (at least, it's hiding some important details). To get your music onto iPod, you use iTunes (just a music organiser). If you want iTunes to rip a CD so that you can put your CD onto iPod, then by default it rips the songs as aac (mp4). This is a superior standard to mp3, but many mp3 players (and windows media player 9 and below, perhaps 10 too?) don't support it. So consequently they don't work. Until the other manufacturers start supporting mp4 (it's really not that hard -- most mobile phone music players support it; my old Nokia that was 2 years old supported it), you can change the settings in iTunes to make it rip your stuff to mp3. Then it'll play everywhere.
As you say, iPod is just Apple's name for their mp3 player, like Hoover and vacuum cleaner. Personally I'm of the opinion that they're better than other mp3 players, simply because their interface is so much easier to use. They're also more popular than any other one, because of good marketing and good design.