Cinematographer vs Director of Photography

Is there a difference?  I don't know.  People believe different things depending on what Planet they're on.  I guess I use them interchangeably.  Part of me thinks that Cinematographer is proper because out of respect for the Director, there should only be one "Director" on set.  On the other hand, I love working with great Gaffers and Best Boys and Grips and "Directing" or leading them - thus, I'd be the Director Of Photography or maybe Director Of Lighting.  OK that's it - food for thought. 

Jeff Scott in Denver