Meaning of Gender

I'm still confused on this topic and the videos and links haven't really cleared it up for me. What is gender? What is it based on? How are we able to identify genders, differentiate genders, and enumerate genders?

The video is defining gender as how someone identifies. Identifies as what? It's not clear what someone is identifying as or with. What is this identifying based on? I could identify as a honey badger, a deity or a celestial being, or as royalty. I don't think anybody would take me seriously in any of those cases and would diagnose me as delusional. Is it identifying with either of the sexes (humans are sexually dimorphic, only producing two types of gametes)?

The Healthline article states that gender is an identity--your personal sense of who you are--while also stating that gender identity is how you conceptualize your gender. What does that mean? Gender identity is how I conceptualize my personal sense of who I am? Wikipedia states about the same: gender can refer to personal identification of own's gender (gender identity), and gender identity is a personal sense of one's own gender. Does anybody else see how viciously circular that reasoning is? It's certainly not edifying.

And then there's this second definition stated by Healthline and Wikipedia: gender refers to socially constructed categories that relate to what it means to be a man or a woman, and gender can refer to social roles based on sex of a person (gender roles). Thus, if we remove the identity part (because what are we supposed to be identifying with), then gender refers to socially constructed categories based on the sexes--man and woman.

How are those categories defined and the roles constructed? Wikipedia further states that gender is the range of characteristics pertaining to femininity and masculinity. Okay, so femininity and masculinity are derived from sex-based categories representing traits typically identified and/or associated in females and males. In short, societies have observed personality differences between the sexes and abstracted away those characteristics into the categories of masculine and feminine. I think that those psychological differences along with physical differences helped define different roles for the sexes, too.

It seems like the idea is that gender is a social construct based on society's ideas of what it means to be a man or a woman. But there's also this idea that gender is something you are or something you possess independently of society's views of the sexes. Like I pointed out above, the masculine and feminine is derived from perceived personality differences in the sexes, so there's something underlying this whole gender idea that originally birthed the socially constructed categories. Which is it? Is gender something intrinsic or something extrinsic? Is gender based on the two sexes and its different combinations: 1) male, 2) female, 3) both male and female, and 4) neither male nor female? Or is it based more loosely around social categories that are innumerable and can be created by anyone?

Any help and answers would be greatly appreciated to help me better understand this. Thank you.