A person who is sexually attracted solely or primarily to others of the same sex.
Sexually and/or romantically attracted to members of the same sex, such as a man who is attracted to men or a woman who is attracted to women; gay. (Typically used in the sense of sole/exclusive attraction.)
Between two people of the same sex; gay.
The state of being sexually attracted primarily or exclusively to persons of the same sex, sometimes (potentially offensive) restricted to same-sex attraction between males.
Sexual activity with a person of the same sex, sometimes (potentially offensive) restricted to same-sex sex between males.