An "undershirt" is old word for a piece of underwear covering the torso, which has fallen out of usage in the UK, but is still commonly used in North America. "Vests" is by far the most common term in UK. "Underpants" or "pants" cover the part of the body where the sex organs are, but never "drawers". Most common words: "shorts " as in "boxer shorts" for the looser fit. "Y-fronts" for the tight fit (UK), "boxers" or "briefs" used for the same things in Canada and the USA.