"Ghost" is more formal ("spirit" being the most formal). "Spook", when referring to a ghost, is considered slang. "Spook" is also a verb meaning to frighten someone or something. "The horses were spooked by the loud bang." "Spook" is also a slang term for a spy, usually from the U.S. Central Intelligence Agency.

Ghost is a noun and Spook is a verb. Don't spook the horse. (scare the horse) There is a ghost haunting that house. (ghost in this sentence refers to a spirit of someone who died)