| regeneration is explained in the glossary of terms in the Monster Manual.
If a monster has Fast Healing, it will regain a number of hitpoints per round indicated in the description as long as it is not (dead? at negative hp? I'd have to check)
If a monster has Regeneration, it can only be damaged normally by certain weapons. All other damage is considered nonlethal damage, and will heal at the rate indicated in the description. Even when that nonlethal damage would take the monster past -10 hp!
A troll can only be truely damaged by acid and fire. All other effects will result in nonlethal damage, which it will regain at a rate of 5 hp per round.
A chain devil can only be truely damaged by silvered or good aligned weapons, or by good aligned spells. All other damage will result in nonlethal damag, which it will regain at a rate of 2 hp per round.
Note that a chain devil also has damage reduction 5/silvered or good, which will reduce the nonlethal damage it gets by 5 points from each weapon hit, but this is unrelated (mechanically) to the regeneration. | 
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