In my culturally and historically inaccurate English that I will force all English speakers to use when I conquer the world (through making games and good cooking) I will decree it should be swimmers (grow up) as a casual term, swimmies as a diminutive casual term.
Swimwear generally. A women's two piece is called a bikini, men's swimwear are called swim trunks if they're full shorts, a speedo if it's just the essentials
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I've heard Swimming Short before, not sure if they were American though.
Swimmers is slang for spermatozoa in the US 🤭