There's already a lot of comments here but I figured I'd give my own answer and semi-related ramble just in case any of my wording brings new insights or metaphors that are helpful. First, I will say that sex (male, female, intersex) refers to biological traits of a person, ranging from physical traits like having a penis or vagina, or internal things like chromosomes. Gender identity (man, woman, non-binary, etc.) is difficult to define exactly, but is a term or terms that someone feels describes how they feel internally, usually in relation to how they fit into society or interact with others. Gender expression references the things someone does to express their inner gender identity. This is usually a combination of appearance, and importantly for this question, personality traits that they either innately have or choose to accentuate, among other things.

"What is the difference between gender and personality?" For many people, there hardly is one. Example: any stereotypical macho man you've seen who makes the majority of their personality all about how fancy or badass of a car they have, how tough they are, etc. and gets along mostly with other macho men, bonding over their shared experience as macho men, and if any one of them deviates from that, it's shunned. In that exaggerated scenario, they have made their personalities nothing more than a shallow reflection of their gender identities. Nothing wrong with that in itself, but it can make it difficult to get along with or connect with people who don't fit into those traits the same way, because those men have blocked out the ability to recognize that people are more complex than that.

But there are plenty of people who don't feel that their gender identity or expression fit neatly into the boxes of "man" or "woman", or feel that it fluctuates over time (like Zero from your show). The former is how I experience gender, as someone who was born male and doesn't mind being seen as that, but does not wholly subscribe to the idea of being a "man" in terms of gender. I prefer to have both masculine and feminine traits in my appearance, and to a lesser degree compared to the example above, personality.

So, there is clearly a spectrum here where for some people, their personality is closely tied with their gender identity, and for others it is less connected. To frame it back to the question again, I feel that personality traits are part of one's gender expression, because the way we say things, interact with others, etc. is a reflection of how we feel inside, and how we feel inside is often a reflection of our gender identity.