Gay, lesbian, etc. are sexualities, which has nothing specifically to do with gender per se. Gender is a performance we do based upon what our culture expects of us based on specific labels and (often physical) traits. Think "goth girl" or "punk" or something. When given a label like that, you probably thought of a specific set of physical traits and behaviors, including fashion, hairstyle, and makeup. That's gender in a nutshell. Sexuality is more "if not attractive, then why x shaped?"

It gets complicated because people really like to put things into an either/or box when life is so much more than a or b. Originally, sexualities were defined as two states: heterosexual and homosexual. Hetero, meaning other, means an attraction to the other sex (generally thought of as the opposite sex/gender due to a lack of information on intersex folk and the aforementioned two boxes appeal in the human psyche). And the opposite would be homosexual - an attraction to people of the same sex. But this is an elementary level of understanding, like when we teach kids about the 3 states of matter and leave out things like plasma.

Because people have preferences and all straight men aren't attracted to 100% of women, and then there's lesbians and gay men and bisexuals and then there's how gender presentation plays into our attraction like with butch vs femme lesbians or how men and women both can appreciate a girl who could bench press them. And then some people are into femboys and women only while some are into men that belong in the Scottish Highlands wearing kilts and claymores and women who own fainting couches and ball gowns and wouldn't even glance at anything outside of those 2 groups, and then some people are only attracted to specific body parts (dick or pussy) but are less strict on who those parts are attached to, and then there's the people who don't care about anything beyond personality, and then...the list goes on and on.

And then it gets even more complicated when you start talking about romantic attraction, because that's entirely its own spectrum as well. People can be romantically attracted to the same or different genders compared to sexual attraction. Some people are sexually attracted to multiple genders but could only see themselves dating one specific gender, some people experience no romantic attraction at all or no sexual attraction, or even both together. The human brain is a massive mess and there's simply no way to easily quantify the human experience - if we even can at all. I saw a post recently that went something like "the brain is 3lbs of mostly fat puppeting a meat suit by using less electricity than a light bulb, and if it can hallucinate algebra into existence then I'm fully willing to believe that it's also capable of identifying its own gender" and I think that sums it up pretty nicely.

Gay and lesbian are not describing gender, but sexual attraction.
Sexual attraction has been traditionally part of the gender identity, as have been other factors like dressing style, hobbies, home and work responsabilities, and a lot more.
Most sexual attraction descriptions are very subjective, because they sometimes describe gender and sometimes sex.