Lesbian A woman who has a sexual and/or romantic attraction towards women. Some women choose to define themselves as gay instead of lesbian.
Gay A man who has a sexual and/or romantic attraction towards men. The term can also be used to describe homosexuality in general. Some women also identify as gay.
Bisexual Someone who has sexual and/or romantic attraction to both women and men. It is often used as an umbrella term which can include any other orientations where there is attraction to more than one gender, whether that be romantic or sexual attraction.
Trans An umbrella term used to describe any gender identity where the assigned sex at birth does not match a person’s present gender identity. Trans* identities can fit within the binary (female or male) or outside of it. There is a whole spectrum of non-binary gender identities.
Queer or Questioning Queer is often used as an umbrella term for people who are not straight or who don’t identify with their assigned sex at birth. People may also identify as queer if they don’t feel that the terms lesbian, gay, bisexual or trans fully represent them. The “Q” can also stand for questioning. This is someone who is in the process of exploring their gender or sexual orientation, is unsure or is concerned about applying a social label to themselves.
Intersex Someone who has a variation in sex characteristics (such as reproductive organs) that may not allow them to be distinctly identified as female or male.
Asexual Someone who does not experience sexual attraction. They can still be romantically attracted to people, whether that is to the same or a different gender (alternatively, someone who doesn’t experience romantic attraction is aromantic). There are many other identities within the asexual spectrum. For example, a demisexual is someone who only experiences sexual attraction when they have a strong emotional connection with another person and a grey-asexual is someone who only rarely experiences sexual attraction and under limited circumstances.
Non-binary A person who does not feel that their gender identity ‘fits’ socially constructed gender roles.
More detailed terminology can be found here