Jack Benny's character on his radio program was notoriously 1) stingy and 2) a bad violin player. In real life, Benny was known as an expert violinist and lavish tipper.
Johnny Carson's schticks include Karnak the Magnificent, an Indian fortune teller who could divine answers to questions sealed in envelopes and kept in a mayonnaise jar on the front porch of Funk & Wagnalls since earlier that afternoon.
Jerry Lewis's schtick was to act like a schlemiel, but in real life (for example as the host of the annual Muscular Dystrophy Assocation telethons) he is generally regarded as a mensch.