Marcus Davis talks about some of the key differences:

“One is the way you stand,” Davis said. “The way everyone stands so upright and staggered. You need to square your hips to defend a takedown. Also, to check a kick, you can’t do that from a staggered stance. You have to center up a little bit, hips pointed forward, in order to check a kick correctly.
 
“That right there takes away a lot of your boxing stuff,” he said. “And then the way you throw punches, the way you move your head. The defense is different. In boxing you lean back and do, like, the fading out of a punch. You can’t do that in MMA. If you lean back, you leave your legs forward. That leg will either be kicked or it leaves the leg open for a takedown.”
 
Davis said one cannot bob and weave because of the danger of being kneed, or of the chance of being caught in a Muay Thai clinch that leaves one vulnerable to knees and elbows.
 
But once he made the transition, Davis said, there were elements of boxing he continued – and continues – to use.
 
“The timing of punches, being able to get into the pocket, throw punches and not get hit, I was still able to carry that over into my MMA,” he said. “Defensively, I figured out what works in MMA and what does not work in MMA. The big thing is head movement. You have to be able to move your head, and you still have a lot of MMA fighters who don’t know that. A lot of MMA fighters do what I call framing up, where they just put both their hands up and keep them nice and tight around their head.”

With every sport that's incorporated into MMA, some of what works in the original sport is bubbled out in the cauldron of a MMA fight. Not everything translates over. We've yet to see anyone effectively work in X-guard from jiu-jitsu, the traditional stance in wrestling where wrestlers bend at the waist to protect the legs and hips and so on. None of this is to say categorically those elements we see in the traditional sports will never make the crossover, just that there's clearly a line of effectiveness some techniques do not cross enough to make them useful. And Davis is right: there is still a ton of room for growth when it comes to applying what boxing (or BJJ, or Thai boxing, etc.) does work into actual MMA competition. When Davis spoke of the "framing", the first person I thought of was Jake Rosholt. So close, yet so far.