I’m in Western Australia, I’ve always called them bathers
Swim suit. Two quick syllables with alliteration.
SE Michigan.
This.
I’m in South Florida now and the same is as or more true here now than it was there then.
I’d say my parlance would be that women wear “swimsuits” or “bikinis”, while men wear “speedos”, “swim suits”, “swim trunks”, “board shorts”, or “shorts” depending on the details.
IIRC my parents tended to use “bathing suit” as the generic for theirs or ours when we were little.
I did not vote.
I consider “swimsuit” and “bathing suit” to be synonymous, and to be broad terms that cover a wide variety of styles for both men and women. The specific style I wear, baggy shorts, are “swim trunks”.
I think it’s regional, too. I’ve never heard anything but “bathing suit” generically for both men and women.
“Birthday suit” is naked; for any gender.
For the men’s version: swim suit or bathing suit for any type; swim trunks for the type that are mostly like shorts, but I wouldn’t use ‘trunks’ for any type with no leg portion.
Female, New York State. Didn’t vote.
That’s me and Mrs. J. on the right, at one of our favorite Kentucky beaches.
It takes a woman with real style to pull off bathing pearls!
I’ve used a lot of the terms for different styles of swimsuits, but the fact that “swimsuit” came to mind just now is probably the answer. If I were packing for a vacation and asked my husband if he was bringing the specific piece of clothing he owns that’s designed for swimming, I’d probably call them “swim trunks” or just “trunks,” since they’re essentially short shorts with loosely fitting legs and a net inside. If they were longer or shorter or shaped differently, I’d call them something else.
“Swimming trunks”, Chicago area
Swimsuit for a man would suggest something like professional swimmers wear rather than the baggy ones that come down near your knee
I think I say “swim suit” more often than “bathing suit”, but one of those two. Grew up in northern New England, now in Missouri.
Swim trunks. DC area.
ETA: Terminology is the same whether they cover what a pair of briefs covers, or whether they are baggy and go most of the way to the knee.
I’ve used both “bathing suit” and “swimming trunks,” depending on how specific I want to be. I’m not sure which I use more often.
I definitely use both more often than “swimsuit.” For some reason, I associate that term more with swimming sports and their more streamlined outfits.
swim trunks, SW Michigan.
Not the requested gender, so I didn’t vote.
I would say “swim trunks,” “swim shorts,” “board shorts,” or just “trunks” for men. If it’s of the budgie-smuggler variety, I’d call it a “Speedo,” regardless of brand.
I’d use “bathing suit” or “swimsuit” for the women’s one-piece version (the two-piece is either a “two-piece” or a “bikini,” depending on the level of coverage).
If I heard the men’s version called a “bathing suit” I would probably expect the speaker to be in their seventies or eighties.
When I was growing up, one of my friends used to call her swimsuit a “swimming suit.” But then, she was old-fashioned and legit lived half her life in the 1930s. 
Interesting. Obviously I am in the trunks camp but small tight I’d call Speedos no matter what the brand, and tight that go down the thighs (worn by many swim training, as in for a triathlon) are jammers to me, not trunks.
But standard issue loose with a liner that go to at least mid thigh are trunks as the go to nomenclature.
Swimming trunks
Svimvear.
Well . . .
Evening vear!
From New York, and bathing suit. I haven’t heard many people call them swim trunks. Swim suit yes, but I’m not sure if that comes from hearing it or looking at the Sports Illustrated swimsuit edition.