Primarily a mobile kitchen is inspected and licensed for cooking. A concession trailer is not licensed or inspected in the same way. I will try and find the legaleze. Well, I couldn't find the actual codes. But, essentially, in a mobile kitchen, you can cook, a concession trailer does not necessarily have the cooking done in the trailer.
For instance, you sell BBQ, and everything you sell is pre-cooked at a commercial kitchen off-site, then you just keep things warm and serve pre-cooked, that does not require inspection or certification for a kitchen. But, if you cook things, like burgers, then you would need the certification for a mobile kitchen.