To us, that knitted top would be considered a vest. The other thing we would consider a vest is the type of sleeveless thing worn over a shirt, but able to zip or button or something like that.
Over here, at least, a tank top is a shirt that has straps instead of sleeves. Most tank tops have wide straps, but some have thin "spaghetti" straps.
A sleeveless shirt {one designed that way by the manufacturer} would not be considered a tank top. A shirt with the sleeves taken off would be a muscle shirt.
