Growing up it was my understanding that Gay meant anyone who is attracted to the same sex- whether that is guys or girls. I know Lesbian but I thought it could be both. Now being more in the LGBTQ+ world it seems like Gay is mainly a label for guys and Lesbian for girls. Right now I feel more comfortable going by Gay Woman (Lesbian just seems daunting for some reason) but I don’t know if that’s correct.
I would say it is correct! As far as I know “gay” equals “homosexual”, which both lesbians and gay men are. So if you’re homosexual you have every right to use it
In my experience I see "gay" and "lesbian" used about the same rate. They can be used interchangeably in my opinion.
If this is what you feel comfortable with, go with it. I have met a number of women who said they are gay. It's totally fine.
Gay is all-encompassing. Though I see lesbian more commonly used, I know women who go by both or either.
The distinction of Lesbian was undertaken - I believe - because men tend to dominate in certain areas of visibility, like in the Stonewall Riots where all lesbians and transpeople have been effectively erased, and so they wanted another banner under which to march so as to distinguish themselves. Personally, I prefer the term "Sapphic," as it relates the female poet who wrote extensively on the subject of female/female love, and it just sounds the prettiest, but Lesbian originates from the isle of Lesbos in Greece, where women who were fond of Sappho - the poet from which the name derrives - and her writings would, for a period of history, congregate. As far as "Gay" goes, though, that's an umbrella term for everyone who has same-sex attraction. I've heard hundreds of women proudly call themselves gay, and I understood what they meant. Everyone does. So if you prefer that term to any other, it isn't incorrect or disrespectful to say so. In other words, go for it!