from the Encyclopedia of Arda:
|Cave-Trolls: The cave-trolls of Moria were of huge size with a skin of dark green scales, and flat, toeless feet. The fact that Gandalf was able to recognise the creature he encountered in Moria specifically as a cave-troll strongly suggests that this appearance was shared by others of the kind. |
Hill-Trolls: A variety of troll adapted for life among hills and moorland. Aragorn's grandfather Arador was slain by them in the hills north of Rivendell, and a company of these creatures were among the armies that Sauron loosed from the Morannon in the War of the Ring.
In appearance they were man-like, but larger, and seem to have been covered with hard scales. They were fearsome and vicious, bellowing like beasts as they stormed into battle, and beating their enemies down with great hammers.
Mountain-Trolls: Apparently trolls that lived in the mountains of Middle-earth. It was creatures of this kind that wielded the great battering-ram, Grond, at the Battle of the Pelennor.
Olog-Hai: A race of trolls bred by Sauron in the later years of the Third Age, seen among the trees of southern Mirkwood, and the mountain borders of Mordor. They were superior to other trolls in almost every way: stronger and more powerful, but also showing greater intelligence and skill. Many of their abilities they owed to being under the direct will of their master, Sauron, and while under his control they could exist in direct sunlight, unlike others of their kind.
In the battle before the Gates of Mordor, Aragorn and the Captains of the West encountered a company of large trolls, identified as 'hill-trolls out of Gorgoroth'1. That battle took place in sunlight, and so it seems to follow that the hill-trolls must have been Olog-hai. They are described as being taller than a man, and covered in horny scales, carrying hammers and bucklers in their claws, though there is no way of knowing whether this description applies to all of the Olog-hai, or just to those in the battle.
Snow-trolls: Trolls adapted for life among snow and ice. No snow-troll appears in Tolkien's work, but we can infer their existence from the fact that Helm Hammerhand is compared to one of these creatures during his sorties against the Dunlendings during the Long Winter.
Stone-trolls: A race of trolls in the service of Sauron. We know nothing for certain of these creatures except that they inhabited the Westlands of Middle-earth: the trolls encountered by Bilbo Baggins and his companions on their journey to Erebor were likely of this kind.
'Stone' presumably comes from the fact that these creatures turned to stone under the light of the Sun.
We know for sure the Stone-trolls turned to stone in sun light and the Olog-hai are not affected by it. What happens with all the rest?