My wife found one huddled in the middle of the road earlier this year, probably only five or six weeks old. Our attempts at fostering have failed spectacularly. She loves it here.
I always joke that I "rescued" my cat because I did get her at a shelter. Only paid adoption fees, and they took care of neutering and first round of vaccines/shots. Absolutely amazing shelter, btw. I had a great experience and I can tell they care so much about the animals.
Anyway! The reason this is a joke is because she is gorgeous and she was going to be adopted immediately no matter what, so really there was no "rescuing" needed.
According to a quick Google search (and how I have always heard it used), neuter is gender-neutral. Castration is the male term, and slaying is the female term. But neuter applies to both.
Well according to the encyclopedia Britannica, and much more importantly; Bob Barker, neutering is when done to a male animal and spayed is when done to a female animal.