plain tank tops are (often) thicker material and usually not rib knit; they are intended to be worn alone with nothing under or over them.
wifebeaters aka A-shirts aka vests/singlets (in UK) are thinner material, usually rib knit and intended to be worn with a proper shirt over them (however, "urban" fashion wears them with no over shirt).
I think it's mostly dependent on the fit. I say that because I also have an outerwear tank-top that is the same color and has the same ribbing as the shirt on the left, but it's the same shape as the one on the right. Unless you're a bodybuilder or something, anything form-fitting and all one color is probably intended to be an undershirt.
Whatever you call them, the looser variety is a must for scorching summers (or sports).