Personally, I'd lump "Gender-as-Self-Concept" and "Gender-as-Social-Role" together, and "Gender-as-Preferences/Personality" with Sex/Neurology. Here's my thinking:
Gender is something we start being instructed and inculcated into, from such an early age, that it's hard to separate that training from our innate nature and personality (if that is even a thing that exists). Gender (as Roles) are a sort of thing one labels theirself with to better define their Gender (as Self Concept), especially when talking about theirself to others, or when making decisions about how they'll represent theirself in public.
Sometimes, people fully buy-in and ascribe to a Gender (as Role) they were assigned when young, whether because of their preference, peer pressure, parental instruction, bullying over non-standard gender expression choices, social pressures put on them before their sense of individuality formed, or whatever else. Sometimes, self-concept is based on the rejection of the "appropriate" or standardized Gender, per societal pressures, which goes on to inform their Self-Concept. Sometimes people revise their Genders during their teen years or adulthood, and do an Ala Carte thing to pick the aspects of Socially-Standard Genders that suit who they are. Sometimes, people invent their own self-concept entirely, or elect not to relate to the Gender of their culture. Just by living within society, and wearing it's clothes and interacting with members who do buy in to the culture, it's virtually impossible to avoid Gender-related baggage in it's entirety. People have no choice but to relate to it, in some way... even if that relationship is to invert it, deconstruct it, or reject it entirely.
Insofar as "Gender-as-Personality", that's something I'd lump with Sex, rather than Gender. I've heard of studies of neurology, and the tendencies and differences between the "Male" or "Female" brain; I'm not sure how rigorous they were, or if any study of the brain can really be separated from the effects of Nurture or Culture... but assuming it's a thing. The general conclusion is that some people have Brains that bias them toward certain activities, certain sexualities and attractions, and so on. Sometimes, people have brains that are more neurotypical for a different Sex than their assigned Sex, and that tends to cause clashes with the Gender Role they're likely to be assigned as well. But "Gender-as-Personality" is more a matter of your brain's physiology, rather than one of cultural norms or training.