Headphone style terminology seems dodgy at best, but I'm trying to determine what company first sold this style of headphone in the US:
I've seen them variously described as "on the ear," "clip on" and "behind the ear." But note that this is not an in-ear sport headphone like they sell in this style now a days. The speaker was half the size of your ear and sat on the outside of your ear, not in it.
These would have been sold for fairly cheap around the turn of the 21st century in the US. I thought it was Philips, but I have yet to find anything online to confirm. In their marketing whatever company it was pushed the fact that it used a new type of magnet which allowed it to be so flat/thin but still have good sound.