Ok I was gone yesterday so this is the first I have seen of this thread. I have kept axotyls, mexican cave salamnders, mud puppies and once a hellbender.
The axotyl that is commonly sold is a neotonic (sp?) tiger salamander that can actually get a little bigger than the transformed version, there are several color varients including albino. the neotonic ones reach sexual maturity without losing their gills and are usually a uniform muddy green or brown, the adult forms are mottled or banded. The largest I have ever seen was one with gills @ 9".
The cave salamander can't be mistaken for anything else, they are slender, duckbilled and albino with very scrawny legs.
T mudpuppies are natives to the U.S. and while not common in much of their range they are widespread. The first I kept was as a kid in North Dakota in a five galon tank in the garage. it froze, in spring it thawed and when I went to dispose of the dead mudpuppy it bit me. They do not ever lose their gills and are about a foot long as adults, They are seldom albinos and have a more flattened head than an axotyl. They are sturdily built and a mottled brown or green though sometimes the mottling is very faint or even absent. With proper care they can live for many years, my great uncle had one for twelve years. They eat just about any small animal that they can stuff in their rather large mouth, I have never had any luck getting them to eat anything that wasn't moving.
Hellbenders are not common and have a much smaller range, They are simalar to mud puppies but up to 1/2 again as large, they prefer faster,cooler water. Other than size the big difference between them and mud puppies is that there is a flap or ridge of skin running lengthwise down the hellbenders body, their bite is painfully strong and they can crush snails, crayfish, and some types of freshwater mussel.
I hope this helps.