I've never heard them called wet suits or rash guards. Here we call them "sun shirts" or "UV shirts". They are most definitely not wet suits like scuba diver gear.
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.)
Rash guards are halfway between a wetsuit and a sun shirt. I have one for surfing, but I got the kids wetsuits because Flathead Lake can be cold as well as sunny. They have more fun and play longer in the water with them.
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.