Nothing really. I think GM might have a trademark on the Crew Cab name, but I'm not certain...What's the difference between a four door pickup and a crew cab?
As it relates to the Dodge's introduction, Dodge tried to play a size game against the competition in the current generation of Rams. Instead of making an extended cab on par with the others (with suicide rear half doors), they came out with a slightly larger cab where the rear door was about 75-80% (?) the size of a conventional rear door and they called it the Quad Cab. They then came back a year or two later and upped the ante on the competitors' crew cabs by making an even larger crew cab dubbed the Mega Cab. But the Mega Cab was too late and many consumers thought the Quad Cab was meant to go against the others' crew cabs.
Judging by this article, it looks like they're getting back in line with the others.