Coloration works like this:
You have your base color: dark [having melanophores] or albino [lacking melanophores].
Then you have genes that work to modify that base: melanoid, leucistic, axanthic, and now GFP.
Axolotls that we call 'leucistic' are not albino, so their base color is dark. The leucistic gene modifies the color. In this case, it stops the color cells from migrating off the neural crest, leading to a white animal with dark eyes and freckles (those are melanophores!). Without this leucistic gene, the animal would be a wildtype.
In albino axolotls, the leucistic gene does the same thing, only there are no melanophores (dark cells), so the base color is albino, and no color cells migrate off the neural crest. So this animal has red eyes, and is white. A white albino = leucistic albino, none of the cells migrate. If you have an albino axolotl that does not display the leucistic gene, it is a golden albino (all the color cells migrate off the neural crest).
Melanoid works the same way: the melanoid gene prevents the creation of iridophores (and greatly reduces xanthophores, yellow pigment cells). This is classically characterized by the lack of shiny eye ring and shiny spots on the gills and tail fin. Any base-color animal can be melanoid as well.
Axanthic isn't something we run across a lot. Non-albino axanthic axolotls tend to be less hardy, and often die within a few weeks of hatching. Albino axanthics tend to be a creamy white, with no yellow spotting that you sometimes see.
