Let me tell you about them.
PsychThe main character of Psych is Shawn Spencer "Psychic Detective". He and his best friend Burton "Gus" Guster work for the SBPD(Santa Barbara Police Department). Shawn pretends to be a psychic, and Gus is his assistant. Shawn's really just very observant and he appears to have a photographic memory. Sometimes he goes places he's not supposed to and "divines" information that the police would otherwise not be able to use. He's dating Junior Detective Juliet "Jules" O'Hara. Head Detective Carlton "Lassie" Lassiter is Juliet's partner, and he disapproves of Shawn's methods. He's my favorite character.
CastleRichard Castle is a bestselling author, a mystery writer. He met (Detective? I'm not sure..) Kate Beckett when there was a killer that copied scenes in Castle's novels. After they solved it, he decided he was going to write a book about a detective named "Nikki Heat", and she was based on Beckett. So Castle follows Beckett around, helping her solve murders. He even has a bullet-proof vest like the police do, only his says Writer instead of Police. Needless to say, I know less about this than I do about Psych.