I believe that if a man and a woman get together and both sides get turned on, the man is more likely to be more desperate to get off.
Is it common among women though?
(Not a woman, just a dude on the internet sharing my experience.)
This really depends on the woman and the man. Sometimes getting your partner off scratches a bigger itch than getting off yourself. I’ve even felt differently depending on the partner I was with or the mood I was in.
As a general rule of thumb, it’s easier for women to cum multiple times in quick succession than for men, and for women to keep going after cumming. So in my experience, women like to cum early and often, while men just want one big orgasm at the end. It’s rare for a man to be able to orgasm without ejaculating, and it’s the ejaculation that makes us need a refractory period.
Then there are trans women as well, who you might think are most like cis men with regard to orgasms, but in my experience, trans women are less concerned with having one big orgasm at the end of the session, and usually more able to cum multiple times and cum without ejaculating.
Again, all of this is just my experience. It’s best to ask your partner what they like and what they want to do with you. Listen to what your partner wants, and prioritize their pleasure. Some people are really easy to “read”, but some are harder, so asking and listening is always the best way to please your partner.