Yep. I don't really like the way Steve said that all "normal" iPods are iPod Classics, because it lead to confusion, like this. You have, very likely, a 5th (or 5.5) generation iPod, though you might have an older one than that. If it plays video, it's at elast a 5G.
However, an iPod Classic is the iPod currently for sale. It comes in 80 or 160 GB flavors, Black or silver, and a metal front.
iPod Photo 40Gb. Black iPod Classic 160Gb.
7836 songs, 49.66 Gb. 31 movies and many more TV shows, 32.4 GB. 13,809 Photos, 21GB.