Gay

"Gay" is a term labelling sexual or romantic attraction.

MLM
Men who are attracted exclusively to other men often describe their sexuality as being "gay". They use the term to say that they are interested solely in other men. The original term for this was "homosexual", "homo-" meaning same and "sexual" referring to a sexual orientation. The abandonment of the term "homosexual" for the term "gay" was likely prompted by the medicalisation of homosexuality. By declaring themselves gay, a term that originally meant happy, men said that they were content with their attraction to other men and that it wasn't a disease.

WLW
Although the generally preferred term for this is "lesbian", some wlw refer to themselves as being "gay women". This is women who are exclusively attracted to other women.

Non-Binary People*
Many non-binary people refer to their attraction to anybody as gay, regardless as to if it is nblw, nblm or nblnb. This is because, as their genders fit outside of the gender binary, there is no "opposite gender" for them to be attracted to. Although "gay" generally refers to attraction to the same gender, it can also mean attraction to a gender which isn't the opposite gender.

Bisexual/Pansexual/Omnisexual/Polysexual people
Although other labels exist for their sexualities, many m-spec people also refer to themselves as being gay. This could be due to the emphasis on gay-ness in the modern LGBT/MOGAI rights movements and communities. The rights for two people of the same gender to be wed was referred to as "Gay Rights" rather than "LGB** Rights" or "Same Gender Marriage Rights". The word "gay" is also heavily emphasised in LGBT communities, as people say that they're "really gay" when around their partner of the same gender.

* this does not include aroace enbies, as they are not attracted to anyone

** the T does not apply here becuase being trans does not impact one's ability to marry.