During ejaculation, semen is ejaculated in a series of rapid-fire contractions of the penile muscles around the base of the anus. These contractions cause the "squirts" of semen that we believe you're referring to. Men tend to prefer a larger volume of semen - or more "squirts" - as each one represents a pleasurable muscle contraction. Plus, many men see a larger volume of semen as a sign of potency. This isn't entirely accurate, as the actual sperm count in smaller ejaculations is often perfectly normal.
And as for women? We'd say that most women do not count how often a man releases cum from his penis when he orgasms. Generally speaking, women are more focused on the sensations that they are feeling at that moment, and are happy that their partner is having a good time.