I don't know a better word for it, but the term does seem to be "bodies" or, I suppose bodysuits. I remember back in the early 90's when we had "bodies". Things like tops but with poppers to do up on your crotch so it held it tight and always looked tucked into your trousers. They sort of look like swimsuits. Well.. I noticed a year or so ago that they came back into fashion somehow. Lo and behold, all the young'uns (I make myself sound old don't I- I'm only 26!) have gone and bought the damn things and are wearing them.
You probably won't catch many people my age or older joining in though, because we REMEMBER wearing "bodies" back in the 90s and we remember why we stopped wearing them. Poppers that rub on your crotch, or lumpy velcro where you really don't want lumpy bits? It undoing in public and pinging out spectacularly, or worse still, hanging out the back of your trousers and flapping around behind you, and you didn't even notice. And then, the dreaded moments of trying to faff around to undo the damn thing to use the toilet. I was too young, but older generations have told me that when inebriated this was a mammoth task and resulted in accidents, and I imagine it was also a real passion killer when getting down and dirty with a guy, having to take off your bodygro for grownups... *cringe*
Rihanna wearing one... Awesome or not? I don't know.
This is all reasons for it to be AWFUL, but it is also awesome, because on the right people it looks stunning... see here:
In searching for photos for this post, I'm afraid I have stumbled upon the monstrosity of the MALE BODYSUIT. I can only imagine how it must feel to have poppers around your nads, and I feel sorry for any men that buy and wear these, and I know that if I was to slip my hand down a guy's trousers and discover poppers, I would be afraid (also my husband would probably be quite cross with me, unless it was him wearing it, and then I'm not sure if it would actually count as grounds for divorce if he thought that was a good fashion choice) *shudder* I can't actually bring myself to save any photos of these men's bodysuits to show you, I will leave it to your own discretion to click the link or not...
http://www.bodysuit.com/mensbodysuit1.html