The iPhone was a small battery powered box you can hold in your hand and it could play music, just like the iPod, but at the time the iPhone debuted, that's about where the similarities ended.
Also, because of its price ($500 plus a two-year contract) the iPhone targeted a different audience.
iPods had just become colour when the iPhone came out, so the main differences were interaction (touchscreen vs "touch wheel"), screen size and connectivity. It wasn't long before the iPod touch came out, with a big touchscreen and apps; basically a non-phone iPhone, giving that different audience a clear transition path.
The iPhone was about combining your music player (that everybody already owned) and with your phone and then adding an incredibly smooth web experience. Without the iPod functionality, it would have still been a revolutionary phone, but the mass adoption and hype surrounding it would have been reduced.