On wiki,
Hairband is for top of head
Headband is for forehead
But in practice these two tags overlap and people just tag both.
Examples:
Hairband that's also tagged with headband
Headband that's also tagged with hairband
Hairband positioned near the forehead
Correct example that features both
Additionally, tags like bow headband are used for bow hairband: https://danbooru.donmai.us/posts/8436818