What is the difference in spay and neuter?

Neutering is done to males - it involves crushing the Vas Deferens so sperm is no longer able to leave the body. It can be accomplished quickly (seconds) with a vet with the proper tool. Spaying is done to females - it involves tying off the Fallopian tubes so eggs cannot enter the womb. It requires a surgical operations and is therefore a lot more expensive and time comsuming.
Neutering is the removal of an animal's reproductive organs; spaying is the same thing, but the term is generally used on females.
"spay and neuter your pets to control the pet population"-

spaying for female, neutering for male.
Two operations to produce a sterile animal. Spay is for females; neuter is for males. Usually the operation involves cutting either the fallopian tubes (females) or the vas deferenz (male.)