Well, they do overlap a bit but they're different topics in purpose, right?
Anyway, I guess I should post my example.
I was DMing (is that even a word? it sounds just.. bad) a Dungeons & Dragons 3.5 ed. session a couple of days ago.
We organized it very quickly, and since I didn't really have time to carefully prepare it I just wrote the plot in a txt the day we played (it was 2 lines) and made up the background of the setting as we played.
It was basically meant to be a dungeon crawl with a very light plot, mainly 'you have to found the MacGuffin because the king (an half-orc, because I found it more fun that way) has been challenged by some other nobles over the throne and has to find legitimacy some way'.
So for the most part, it went like that, with the occasional tongue-in-cheek humor and 2 good maps provided by the lovely random dungeon generator.
Then the player's laptop I was using to keep the map in check was slowly overheating and we had to turn it off.
Since I couldn't just stop the session I had to cut off the second level and retool the plot on the fly, with them quickly finding the artifact and going back to the king just to discover that the old woman who gave them the hook about the artifact (which, I feel the need to point out, was a sentient talking crown) before she could even tell them and in fact it was the other long lost heir to the throne who was planning to destroy the reign to avenge the fact that he was aborted (the idea may sound stupid, but in fact it's even stupider) that told the players about the crown.
After having realized that both the heirs were utter morons.. well, this is when things started going to hell.
While I desperately tried to throw solution after solution to the players, they were too busy discussing what they should have done for the good of the kingdom, with one of them convinced that he should become king, the paladin/monk that insisted that the kingdom should become a republic and the druid that got bored and left them to explore the world with his animal companion.
Even after I organized (in-game) an official discussion between all the major factions of the kingdom (again, all invented on the spot) they just couldn't find an agreement, so I had to stop the discussion in some way and threw in some orc invaders commanded by the dark lord that was trying to conquer the lands (original, huh?).
The paladin escaped to go to the monastery and tell them about it, while the thief/warlock kept the crown, killed the orcs and crowned himself king.
And that's how it ended.