Just like to point out, there are no such things as forest trolls in Middle-earth.
The different names for trolls seem just to refer to where they live, and slight possible physicall differences (ie, snow trolls are white) - basically like you get snow leopards, normal leopards, black ones, etc.
The only truely different-from-Hobbit/Moria-trolls were the Olog-hai, who have no problems with sunlight as long as the will of Sauron is on them.