Down under we call the rash vests, or "rashies". They're typically a thin neoprene like material, often as thin as a t-shirt, but some can be a bit thicker for warmth too.

Oh, rash guards are most definitely not wet suits, I wasn't intending to imply that. Just for what the parent was using them for (protecting kids while doing what sounds like playing in the lake) they sound like they'd be a better fit than a wet suit.

"UV shirt" would be a far more sensible name than "rash guard", I admit. That was just the name I learned for them when I first found out they existed. (Which was in Hawaii, under a brutally unforgiving sun.)