Stage 1: Task resolution is about small things and conflict resolution is about a bigger thing. I then read several posts specifically saying the difference is not about the scale of the conflict, so I evolved to:
Stage 2: In Task resolution, a failure means X does not happen, but in conflict resolution, a failure means Y happens. After more thought, this seems like it had more to do with stakes setting than task vs. conflict resolution, so then I moved to:
Stage 3: The differences between the two is more of a dial, than a switch. To quote Vaxalon from story-games post from Sep 11th 2006
"Resolution can be nested.
Let's take a standard DnD combat. The heroes are bursting into the evil temple to rescue the princess.
In the middle of the fight, stop time right where the fighter is swinging his sword at a temple guard. Here's some of the layers that may be in play at that moment:
"Does my blow hit the guard?"
"Does it do enough damage to remove him from the fight?"
"Do the guards keep us from getting to the altar before the priest sacrifices her?"
"Do we save the princess?"
At what point does it become conflict resolution?
I would argue that it becomes conflict resolution when the answer is nontrivial. "
But this means that the definition is dependent on the individual's tastes about what makes something "nontrivial".
I was still unsatisfied about the differences and I started to write up my thoughts when I came across Eero Tuovinen's thoughts from story-games, Feb 2010. This has everything I wanted to say, but could not put together. Thank you Eero, for clearing it up for me.