The other term used by underwear companies such as Jockey® is an A-Shirt as opposed to a T-Shirt. I don't wear them as an undershirt, but on occasion do wear them when working out as the ribbed variety are lighter in weight with a tighter fit compared to a standard tank top which often have wider straps at the shoulder or other styles of sleeveless muscle-type shirts. Of course they look smoking hot and especially on the right guy! YUM!
I always assumed that the colloquial name was derived from A Streetcare Named Desire.
Here in classic white:
They look hot in black as well:
And even in in between grey!