Koss on-ear headphones?
Headphones
A community for discussion around all topics related to headphones and personal audio.
Headphones.
They're called headphones. On-ear or over ears.
But headphones
On-ear headphones are known as "supra-aurel"
OP is not looking for on-ear headphones, but earbuds with a headband.
Like the Sony MDR-A43L
If the Walkmans I picture in my mind are right, these are called on-ear headphones
A picture would help, are talking like the ones that came with the aiwa portable CD players?
headphones.
Hey, belated comment: Sony invented and called that design "vertical in-the-ear."
Because it's got a headband, it can set the speaker driver perpendicular to the ear canal instead of covering the ear canal opening like regular earbuds, and this creates the impression of extra clarity.