Similar to another poster, I break it down like this:
-
Sex is your physical binary biological gender. If you have a penis and testicles that produce sperm, you are a dude; if you have a vagina, ovaries, and a womb to carry a baby, you are a female. No ifs, ands, or buts about this imo.
-
Gender identity is what you identify as. This is where we go he/she/they, and can be completely removed from the biological sex of the person because gender is psychological and belongs to the sense of self. We use “he” and “she” as binary identifiers of male and female species respectively, but with humans it becomes more complex as perhaps a male may identify as a female-gendered person, or a female may identify as a male-gendered person - or both of them identify as a non-gendered person.
-
Gender roles could (and I personally think should) be separated from both biological sex and psychological gender. This is what we, as human society as a whole, determine the division of labor and what activities, habits, and behaviors are acceptable for men and women. In the past when we were still growing as a species, this was actually important since men were needed to hunt down animals due to biologically being more suited to it and women were needed to do other things while the men were out; nowadays, however, this is a dated concept as anybody can earn money and we don’t live in a world where we need to hunt to survive. Women can just as easily put food on the table and enjoy riding motorcycles or chopping down wood just as easily as men could stay at home, clean the house, take care of the kids, and cook meals for the family for when their partner gets home. If anything, I would say that we could consider the “Masculine/Feminine” dichotomy as a sliding scale at best, but what society considers “masculine” or “feminine” changes all the time, so it’s arguably ultimately worthless trying to categorize this.
TL;DR Biological sex, gender identity, and gender role aren’t all mutually inclusive. If I am a man, I am not beholden to the expectations of being a macho man who slams IPAs and lifts weights while talking about cars; on the flip side, if I am a man who identifies as a female, I am also not beholden to obtaining a Blåhaj shark plushie, wearing kneesocks all the time, losing 60 pounds, and becoming a software engineer who only runs Arch or some other Linux distro.