Maybe there was a regional difference in terms. What some Floridians may have called water snakes instead (sounds kind of generic), we called water moccasins. They don’t have the line in their eyes or such a pointy, triangular head. In south Texas, Arkansas and Missouri, though, their markings are otherwise very much like the poisonous ones. We did call the poisonous ones cottonmouths.
I guess the terminology doesn’t matter so much.
The poisonous ones usually swim more slowly when on the surface. Before biting, they most often lay in wait and aren’t seen in advance. Way back when, some old time noodlers gave the mistaken advice that cottonmouths could not bite when under water, and new noodlers were advised to duck under when seeing a cottonmouth. Bad advice, in my opinion.
The non-poisonous ones swim a little more quickly on the surface and are usually (but not always) seen swimming away.
The only venomous snake in North America which has round eyes is the coral snake. I know they have them in East Texas as well as Florida. When I was in high school, a Ranger at Eglin was bitten by a coral snake. They literally used an F-104 to fly anti-venom from New Orleans. The Ranger lived.
I was always taught the rhyme: Red on yellow, kills a fellow. A coral snake had red lines surrounded by yellow. A king snake does not. I used to have an old momma cat who would kill coral snakes and feed them to her kits.
BTW, that is me holding the 7 footer with the rake.