There is a variety of sleeveless T-shirt that is called a singlet Down Under (maybe in Britain too?), and a muscle-shirt (mostly on males) or tank-top (mostly on females) here in the New World. It's a little-known fact that a black singlet is a culturally important signifier of New Zealand-ness. Google suggests that on these shores, a singlet is what wrestlers wear.
I gather that these days some people are calling these things "Wife-beaters" because of their appearance on the perps in reality/cop TV shows. A living language, you gotta love it.