As I mentioned in the concurrent thread, those aren’t distinct “genders”. They’re phrases representing various preferred ways for people to describe their gender identity.
In consequence, there’s not likely to be any formally standardized meaning assigned to the differences between those descriptive phrases, and different people will use them in different ways. For example, some people use the asterisked form “Trans*” to suggest a less rigidly binary perspective on transgender. Some people prefer the term “Transgender” to “Transsexual” because they feel it emphasizes that the “trans”-ness is in their gender identity, not their biological sex. Some people don’t like the shortening of the terms “Transgender” and “Cisgender” to “Trans” and “Cis”, while some people prefer it. And so on and so forth.
“Two-Spirit” is a term originating in some Native American culture(s) and representing cultural traditions of third-gender or other gender-variant identity. I don’t know to what extent (or by whom) it’s considered unsuitable “cultural appropriation” for non-Native people to use the term.
Hope that helps somewhat. There are likely to be lots of different opinions about subtle shades of meaning or outlook represented by the different descriptors, and probably there will be few strictly “factual explanations”.