Dyrone said:
I see it every once in a while...could just be a bra...but it seems like it's a little more than that? Like it would be somewhat socially acceptable to wear that thing outside.

It's funny how that goes, those cover less than regular bras but nonetheless do seem more acceptable in public.

Bras that show off cleavage are known as balconette, but we don't have a tag for that. They're just mixed in bra.

I don't think there's any specific name for bras that are meant for public use. Sports bra and bra top both cover more, so not applicable to those two.

klorpa said:
Would bandeau or strapless_bra work?

Bandeau is basically a single strip of cloth draped over the breasts. If there's separate cups, it doesn't apply. Strapless bra might work, though those aren't usually meant to be worn in public.