The party gets hired for some work. In the course of fulfilling their contractual obligations, they slowly start to unveil a much larger plot. This plot entails the fate of an entire region and they become major actors in that scheme. At that point, they may have aroused the interests of several competing factions. Some want them as allies, while others will be glad to hunt them down.
The sense of dread in my games is really high. The players often feel they don't have quite enough to fight their enemies. They are constantly managing their meager resources. Rushing head first, as opposed to careful planing, often results in dire consequences.
To me, that style of campaign would be labeled as dark heroic fantasy. Since, it does feel like a cross of at least two popular literary genres. The characters are heroes but at the same time, the world around them is not quite what it seems. There are a lot of 'things' lurking in the shadows.
This style is truly not for everyone. I have had people that liked it, and looked forward to the games, while others totally despised it.
It is a matter of taste. It is not because a person doesn't like that style that he is a bad player. Often times, these individuals are merely looking for something a little lighter.
That is why I make sure to clearly state my GMing style to the players. If I run a game, chances are, it is a dark heroic fantasy campaign.