Spayed, of course, is when even the urge to mate is taken away- so human beings do not get spayed. They get only the capacity to bear young taken away.
Same with 'neutering'. Male animals get neutered- human males get the duct cut, so the urge to mate is intact, only the means to reproduce has been compromised.
As you all know. But it bothers me to hear those phrases tossed around so freely and inaccurately. You can say you got yourself 'fixed', though!