Gender fluid falls under transgender. Pretty much anything that is not cisgender falls under transgender except perhaps agender (the sense of not having any gender at all.) though there's a case to be made for even that being under transgender because it is differing from assigned gender at birth.
Robin, changing "gender completely and permanently" is transsexual, assuming you mean you change from male to female or female to male.
Usually I'm a big fan of people doing what they want and setting their own rules, but when it comes to language, I become less loosey-goosey because we can only communicate if we use reasonably precise definitions.
