As for what they mean,
we know Axanthic = no yellow pigment
like the Axanthic Halmahera in the original post
For more examples, here's how they work in boas.
Albino or Amelanistic = no black ("normal albino" "T- Albino")
What we normally call "Albinos" are T- amelantistics meaning no black pigment at all. This is what we'd call an albino boa:
T+ Albino ("Caramel albino") = black is present but processed differently = purple tint
It takes a little training to be able to spot this one and is harder to learn to do in photos.
T stands for tyrosinase which is an enzyme that controls how the melanin is processed. In T+ albinos, the melanin is still present in the animal but is processed differently usually resulting in a faded "purple" look. These are often called "Caramel Albinos." Several different strains of T+ albinos are present in Boa constrictors alone. There are also T+ ball pythons, burmese pythons and I'm sure many more. This is a VPI line T+ Motley Boa:
The Motley trait is the checkerboard pattern. The coloration is from the T+ trait. As I said, there are several incompatible strains of T+ in boas. This T+ boa comes from the VPI strain of T+ boas named after the reptile breeding facility (VPI) of Dave and Tracy Barker. Tracy Barker is the one one who established this line as well as did MANY other AMAZING things with reptiles and also happens to be a very nice lady.
Hypomelanistic ("hypo") = less black, more red
Hypo really just means "less" but is usually short for hypomelanistic meaning that the melanin is there but has been reduced. This allows for the other colors normally covered up by the black pigment to show more prevalently. For instance in boas, there are many areas on their bodies which seem brown because there is both red and black pigment present and mixed together. If the melanin (black) is reduced, the red shows through better and "hypo" boas are typically more red than normal boas. This is a hypo boa:
Ghost = Anerythristic AND Hypomelanistic ("hypo") = no red, reduced black
Ghost is a tricky one because it means different things in different species. In boas a ghost is actually two morphs together in one snake: Anerythristic (no red) and hypo (reduced black). In ball pythons, it's a single gene and is also often called "hypo" just to make thing confusing. This is a Ghost boa:
These things vary from species to species because some of these are scientific terms and some are marketing terms and some are scientific terms that have been changed to be marketing terms.
They also vary from species to species because the traits sometimes work in different ways in the different species.
In addition, the base color scheme of the "normal type" determines what traits will be more visually distinct. An example of this would be Axanthic (no yellow) vs anery (no red). In ball pythons, the Axanthic trait serves as the anery trait in boas. AFAIK, there is no anery Ball python. There doesn't seem to be too much red in BPs and manipulating the yellow pigment yields a more dramatically different animal. This seems to be the same with gigas. In boas (again AFAIK) there is now axanthic trait. Since wild type boas often have lots of red in them the presence of the anerythrristic trait which reduces the red pigment changes the visual appearance of the animal more dramatically.
As the individual traits are isolated and understood, the next step is "designer morphs" which are the mixing of multiple traits into one animal. For instance, when we bred boas, we were within the first 2-3 breeders in the world to produce Snow Motleys (three visual traits=Motley, Anery and Albino) and then the next year Moonglow Motleys (four visual traits=Motley, Anery, Albino and hypo)
This is what may have happened with the animal in this post. I suspect it is visual for both Axanthic and T+ because both of these traits have been present in Halmaheras for years. Plus, since they are not stark which like albinos, it is likely that these animals could exist and breed in the wild. In boas, there were many naturally occurring ghosts found in Nicaragua. These animals were visual for both hypo and anery and both of these morphs were prevalent in WC shipments.
There are so many species that have many different traits that have been established, it can be helpful to take a look at them to see what the possibilities are for BTS. I recommend checking out the morphs in: Corn snakes, Boa constrictors, Ball pythons, burmese pythons, reticulated pythons, blood pythons, Hognose snakes, green iguana etc..
To make it even more confusing, you really have to know what the wild type looks like to spot the differences. As we discussed in the other post, if there is a lot of variation in individual specimens in the wild types, that makes things more complicated. If there are regional variations, this is even more complicated.