The Tony Stark character, billionaire-industrialist-brilliant-engineer superhero, has existed in the comics since 1963, 8 years before Musk was born. So, the claims of Musk as a model for Stark are best taken with a grain of salt.
Most likely, the Iron Man movie team -- including Jon Favreau and Robert Downey Jr. -- just finds it helpful to reference Musk as a modern Stark-archetype. (Starketype?) The original Stark drew from Howard Hughes, but Hughes isn't as familiar to the movie's modern audience. And, our other modern billionaires, like Gates and Jobs, don't quite have the same rockets-and-motion pedigree as did Hughes and now Musk.
Howard Hughes is very much the same type of man as Musk. He was at the forefront of both movies and aviation, both of which were young industries at the time.
A lot of attention is focussed on Hughes' later years when he turned basically insane, but in his productive years he pushed forwards the design of the airplane and motion pictures.
If anyone is unfamiliar with his work, I'd recommend picking up a biography and giving it a read.
I keep hearing the Iron Man thing, but honestly I'm not sure I see it. I've seen interviews with Musk and he's way less cocky and more down-to-earth than you'd expect with that basis of reference.