There are actually two classes each of Trophy and Hammer Trucks:
The big difference between the Trophy and Hammer classes is the Trophy is 2wd and the Hammer is 4wd (must have a transfer case). The Hammer Trucks are built to be used in both desert racing as well as rock crawling. There are a lot of little differences between the two classes as well as a lot of little differences within the Trophy and Hammer sub-classes themselves. I believe the Trophy Truck and Hammer Truck Unlimited both are completely open as far as what kind of engine they can run, etc. The Spec/Limited class of each pare this down a little and give specifics in this area. Like I said, there's a lot of little differences between classes and sub-classes.
For extra information, you can also look at the SCORE International Website