Here's Wikipedia's answer:
"Neutering" is often used incorrectly to refer only to male animals, but the term actually applies to both sexes. The male-specific term is castration, while spaying is usually reserved for female animals. Neutering - Wikipedia
I agree with all that Ewie and Loob have said above. I will add that "spay" is the canine equivalent of a human "hysterectomy".
Addendum: The purpose of spaying is to avoid reproduction. Also it reduces the mess associated with the menstrual cycle and the nuisance of male dogs hanging around due to the scent.
The purpose of neutering males is more often than not to avoid, or an attempt to end undesirable behavior such as aggression, male dominance or "excessive expressions of romantic desire" . The neutering works far more effectively if done prior to the arrival of the unwanted behaviors (six to nine months of age). It also avoids entirely testicular cancer.