What exactly does it mean when a person has a dry sense of humor as well as having a dry wit?

Actually you're incorrect. I happen to have a dry sense humor at times. My humor is interchangeable. It can go from dry または extremely wacky depending on mood.

A person with a "dry" sense of humor often says funny things with a serious, calm expression. They don't smile, laugh, または make silly faces. That is the definition of dry humor.