Okay quoting might be easier.
So I've got a list that I think is useful, but I think one thing should definitely be made clear
Labels are subjective. There are going to be people who use labels in different ways, and that's okay. There doesn't have to be a strict definition of bisexual. Anyone who feels that they are bisexual can call themselves that, whether they like men and women, women and enbies, or all genders.
Anyways here's the list, and what I think would be useful to say
Gay: Someone who likes people of their own gender. Usually used to refer to someone who exclusively likes people of their own gender, but not always.
Lesbian: Women who love women. This can be more broad, usually including enbies who love women, and bisexual women. There is also the umbrella term 'Sapphic' which basically is just a more broad version of lesbian.
Bisexual: Many definitions exist, but the best one, I think, is someone who is attracted to two or more genders. This can include people attracted to all genders, not just men and women.
Pansexual: I saw a lot of confusion about this vs bisexuality, so I'll explain this one in detail. A pansexual person is attracted to someone regardless of their gender, while a bisexual person is attracted to someone because of their gender. For example, a bisexual person might love men, women, and/or enbies. Meanwhile, a pansexual person just loves people, with their gender not being a factor. It is common, however, that pan people call themselves bi (though not much the other way around), and nothings wrong with that.
Asexual: Someone who does not feel sexual feelings toward anyone. This does not mean they don't feel attraction or love, however.
Aromantic: Someone who doesn't feel romantically attracted toward anyone. This doesn't mean they can't feel other forms of attraction or love, however I honestly don't know a huge amount about how that works, I'd probably research that more if I were you.
(Allosexual/alloromantic is the opposite, and basically the "default", where you do feel sexual/romantic attraction toward some people. There's also an in-between state, called Greysexual/romantic, however I don't see it used much, and don't know much about it.)
Sexual vs Romantic: I've been saying 'bisexual' and 'pansexual' and stuff, but there are kinda like two forms of each of these things. This applies to homo/heterosexual as well. There's the ...sexual suffix, which means that it's relating to sexual attraction, and the ...romantic suffix which means that it's relating to romantic attraction. Most gay people are both homosexual and homoromantic, meaning they both feel sexual and romantic feelings to people of their own gender. However, someone might be homoromantic and asexual, meaning they feel romantic feelings toward people of their own gender, however they feel sexual feelings toward no one.
Demisexual/romantic: Someone who doesn't feel sexual/romantic feelings toward someone until getting to know them really well. This isn't "just what everyone feels", though many people assume it is. Someone might look at an attractive person, and immediately feel sexual feelings. They also might have a crush on someone they don't know very well, feeling romantic feelings. However demisexual/romantic people don't (depending on which one it is)
Okay, that's sexuality, onto gender
Transgender: Identifying as a gender that is different then the one they were assigned at birth. (Often called AGAB, or Assigned Gender at Birth). This takes many different forms.
Cisgender: Basically just not transgender.
Non-Binary: Identifying as a gender that is not male or female. Often abbreviated as enby. Often use they/them pronouns, but not always. This can many different forms, which I'll go over below. Non-binary people are inherently transgender, although not everyone thinks so. (While this could be a case of people choosing not to use the label, I have reason to believe that it's actually people being enbyphobic, and refusing to include non-binary people as trans)
(I wish I could describe these better, but the only non-binary people I know in real life are genderfluid, so I don't know that much about other non-binary identities)
Agender: Not having a gender at all. This is a non-binary identity, of course. Usually use they/them, but might be okay with any pronouns.
Bigender: Being both male and female. Another non-binary identity. Do note that this isn't necessarily equal. A bigender person could feel like 75% male and 25% female or something. (Percentages wouldn't actually be used, they're just a crude way of imagining it) Might use they/them, but also might be okay with any pronouns.
Demigender: Demiboys/demigirls are people who feel somewhat male/female, but not completely. Using the percentage model, a boy might be 100% male, while a demiboy might be 70% male, and 30% agender. Of course, the values would be different for different people, and again, this is an imperfect model. Often use either he/they pronouns, or she/they pronouns (where either gendered pronouns or them/them pronouns can be used, although only one of the two sets of gendered pronouns). This is another non-binary identity
Genderfluid: Someone whose gender is different at different times. This can take the form of someone being male some days and female other days, or a more complex system in which they feel differently levels of masculinity and femininity at different times, not necessarily all the way one or the other. Some change their pronouns depending on how they feel, while others just use they/them, while still others might have their own set they prefer. Genderfluidity is one of the most varied non-binary identities, so everyone's going to be different.
Xenogender: An admittedly rare non-binary identity that I don't know much about. Basically, it describes someone whose gender is not derived from masculinity or femininity at all. It's completely unrelated, but still exists. They often use 'neopronouns', such as xe/xem or ze/zir. Even if you don't really understand, try to respect it.
A few other terms should be noted.
Gender dysphoria: A feeling of distress caused when one's gender identity is mismatched with their current situation. Can be caused simply by being in a body that one doesn't like, or by being called a gender that you don't feel applies to you. Do note that not all trans people feel gender dysphoria, however many do. Typically, the only way this is alleviated is by transitioning, described below
Transitioning (as it pertains to transgender people): The changing of oneself to align with one's gender identity. For example, if one feels uncomfortable with one's body, one might take hormones or undergo surgeries to make one's body align with their identity. This also encompasses social transitioning, such as coming out to people, and asking them to call one by a new name and pronouns, as well as legally changing one's name and gender. Even wearing new clothes that one feels fits ones identity more would count.
Queer: While it was once a slur, it is now an umbrella term used to describe anyone who is part of the LGBT+ community. (Some older people might still consider it a slur. If someone doesn't want to be called that, you should respect it)
Let me know if you have any questions, because this is a lot, I'll admit.