They are different items altogether.
A creature would (IIRC) gain the benefits of regeneration for any nonlethal damage taken from sources that don't cause actual harm while fast healing would restore the damage that did harm them. So in the case of the troll, anything other than fire and acid would be handled by regeneration. Fire and acid would be subject to fast healing.
In terms of fast healing from 2 sources, they would overlap (same effect). So a creature with fast healing 1 that becomes a vampire (fast healing 5) would not gain fast healing 6. Instead they would have both simultaneously. If by some chance their vampiric abilities were blocked or turned off, the fast healing 1 would still be present.
DC