Pretty sure the 1st iPod had the click wheel. It was a mechanical wheel with a separate button in the middle to click.

The 2004 ones were touch wheels with tap sensors

Yes, but it's the 4G and successors that AFAIK had the selector that was dubbed the "Click Wheel." Previous models had a mechanical scroll wheel that looked somewhat similar and which incrementally added touch functions but when people talk about the click wheel they're normally referring to the tap sensors in the iPod Mini & the 4G and followons.