A neuter (or orchidectomy in doctor speak) is the the surgical removal of one or both testicles from a male. In veterinary medicine we almost always remove both testicles as our goal is surgical sterilization, or the prevention of reproduction. The surgery does not require opening the abdomen unless a testicle has failed to descend into the scrotum during maturation, a situation called a cryptorchid or "crypt". Dogs or cats undergoing a neuter are given pain medication, placed under anesthesia, and the testicles are removed. The procedure generally does not result in severe pain or swelling and patients are able to go home that same afternoon. Benefits to neutering include reducing aggression and roaming if done prior to sexual maturity and preventing prostatic enlargement in older dogs.
A spay (or ovariohysterectomy, yep - it's a mouthful!) is the surgical removal of both ovaries and the uterus from a female. The ovaries are located near the kidneys so the abdomen does have to be opened making recovery a more lengthy process - a female dog or cat should be kept quiet for 2 weeks following a spay to allow her incision to heal. We also keep spay patients overnight to provide additional pain medication if needed, recovery time from anesthesia, and a quiet environment following surgery. Early spaying between 4-6 months of age prevents a female dog or cat from starting heat cycles. Not only does this prevent unwanted litters, it also reduces risk for a potentially life threatening uterine infection called a pyometra, and evidence suggests it may decrease risk for development of mammary cancer - plus you won't have to deal with a female bleeding during heat or attempting to seek a mate!