Both options are acceptable here ( we are close to Siesta Key FL) Boys in board shorts generally wear underwear sometimes they may or may not get in the water but just hang out. I've cut the lines out of MANY swim trunks because they chaff generally the wear sport boxer briefs Ive never seen board shorts w/ underwear as red neck around here at least. Lots of boating beach kayaks skim boards and paddle boards.
https://www.costco.com/Speedo-Boys-W...100427976.html -- those swim trunks are DA BOMB the liner is actually like sport fabric boxer briefs