The two hours was how long before the quest was simply removed if you didn't assign anyone to it. The two turns is how long it will take the assigned companion to complete the quest.
As near as I can tell, one turn lasts as long as it takes for you to advance any of your quests. So complete one stage in a quest and you'll move into the next "turn".
It's the one aspect of the Stronghold I have never liked, personally, but I can see why they didn't just tie quest completion to the world clock; if they did then you could power-level your companions just by constantly resting and let them steamroll through content that's now too weak to challenge them.