Generally yes, with a few minor exceptions.
A person is homosexual if they experience physical and romantic attraction only towards others of the same sex. For several decades, the word ‘gay’ has been considered to have the same meaning.
The word is used slightly more for homosexual men than for homosexual women, however. It is more common to hear reference to ‘gay men’ than it is to ‘gay women’ – homosexual women are more often just referred to as ‘lesbians’.
The word ‘gay’ is also sometimes used in a derogatory or comedic sense for things that are nothing to do with homosexuality. This can sometimes imply a degree of animosity towards homosexual men, but sometimes not.