Many harmless water snakes are confused with venomous water moccasins. It's usually impossible to distinguish between the two while they are still alive i.e. sadly it's only after they are dead that harmless snakes are identified as non-poisonous.
Quick summary (followed by photo info)
(1) Water Moccasins have pits between the eye and nostril on each side.
(2) Water Moccasin eyes are cat-like - egg shaped pupil. Harmless water snakes have round pupil.
(3) When swimming in the water, moccasin head and body show while a water snake head is all that usually shows.
(4) Moccasin heads are large block / triangular shaped while harmless water snakes have slender, elongated heads
See the 4 minute snake video (on youtube) that shows close up video of a harmless water snake (btw: video contains most of the info on this page). As soon as I catch a moccasin - I'll add another video for 'video comparison'.
Water Moccasins are pit vipers i.e. they have a pit (small depression) between the eye and nostril on each side of the head, midway between the eye and the nostril. Nonpoisonous water snakes do not have these pits. BTW: the pit is used to sense heat in their prey.
The pupil of a nonpoisonous water snake is perfectly round. The pupil of a water moccasin is vertical elliptical cat like shaped pupil (egg-shaped or silted eyes like a cat).
Moccasin heads are wide / triangular shaped and they have a distinct neck. The harmless water snake does not have an obvious neck and it's head is slender - elongated. BTW: It's not uncommon for the harmless water snake to flare his head when in danger so it sometimes appears to have a broad head.
On the underside of the tail of pit vipers scales go all the way across in one row (except on the very tip of the tail which may have two rows in some cases). On the underside of the tail of all nonpoisonous snakes, scales are in two rows all the way from the vent of the snake to the tip of the tail.
 While swimming: If just the snakes head is showing it is probably a harmless water snake. If the body is showing too it could be a water moccasin.
 Moccasins bodies are very thick and heavy for their length while harmless water snake bodies are more slender for their length.
 A cotton mouth water moccasin has a white lined mouth - that is positive identification - and obvious if the snake is aggressive (e.g. opens mouth in a aggressive manner).
 Snakes in trees on limbs are likely harmless water snakes i.e. moccasin don't like to climb on tree limbs (they like the bank or a log). Water snakes like to climb on tree limbs.
 Water moccasins tend to move slower and don't seem to fear you - when you approach them. While harmless water snakes tend to move much faster but usually in the opposite direction. A moccasin usually will continue on it's way and is usually not as aggressive as some people 'advertise'. However, if you stumble upon on their babies / family, the mommy snake will come after you. i.e. their reputation for always being aggressive is just not true.
 Fangs are obvious in a moccasins mouth.
 Myth: Snakes can't bite underwater. While it's true that they can bite underwater it's not likely unless they are in danger / trapped.
Another photo of a harmless water snake