I suggest you take a few minutes to reread Vincent Baker's old post on these two types of resolution. A small quote:
Which is important to the resolution rules: opening the safe, or getting the dirt? That's how you tell whether it's task resolution or conflict resolution.
Task resolution is succeed/fail. Conflict resolution is win/lose. You can succeed but lose, fail but win.
The distinction between CR and TR has been important, historically, because it made people rethink the way roleplaying games worked. But we are now in a position to see clearly that CR and TR are, in fact, identical. There is no difference between the two. As analytic tools, they are useless.
Distinguishing TR and CR went like this. First, you ask what the character is attempting to do. This is the task. Then, you ask why the character is trying to do that; or, almost equivalently, why the player is trying to have the character succeed at the task. This is the stake of the conflict.
Then we define: TR is about resolving the What. CR is about resolving the Why.
So, TR and CR are different precisely in so far as we can distinguish between a What and a Why, between an action and the goal of that action. But when we think about this some more, we will see that this distinction breaks down completely.
The character attempts to open the safe. Why does the character attempt to open the safe? In order to get the dirt on the villain. Ah - so in attempting to open the safe, the character is attempting to get the dirt on the villain. Why does the character attempt to get the dirt on the villain? Because he wishes to blackmail the villain. Ah - so in attempting to get the dirt on the villain, the character is attempting to blackmail the villain. Why does the character attempt to blackmail the villain? Because he wants the villain to release the character's little sister, whom the villain has kidnapped. Ah - so in attempting to blackmail the villain, the character is attempting to free his sister. Why...
You will see the point by now. The structure of task and conflict is not that of a simple duality, but that of an infinite regress. Every action (the What) points towards a larger goal (the Why) which gives the action its value. But this goal immediately furnishes a new description for the action, thus becoming a What. This What points to a new Why. And so forth.
When do we have Task Resolution, and when do we have Conflict Resolution? It would be completely arbitrary to say that the task is opening the safe, and the conflict is getting the dirt on the villain. We could just as well say that the task is to get the dirt on the villain, and the conflict is to free the character's sister. We could just as well say that the task is to make a set of complicated movements with the characters left hand, and the conflict is to open the safe. There is no natural division.
But what if we state the whole thing on the level of the player, instead of the level of the character? (This obviously does not help, since the logic of the situation stays the same; but we will discuss it in order to make things clearer.) TR is about things the player does not care about except in so far as they point to something else; CR is about things the player cares about for themselves. The player doesn't care whether he opens the safe or not, but he does care about whether he gets the dirt on the villain or not.
The counterargument stays just the same. Perhaps it is true that the player only cares about the action (the task, the What) because it is a means to a goal (the Why). But this goal can itself be seen as a What, which points to a further Why. The player does not care about getting the dirt on the villain, he cares about freeing his sister. He does not care about freeing his sister, he cares about being able to think of his character as some who looks after those he loves. And so on, and so forth. The only way to stop the infinite regress is to postulate at some point the "Final Care" of the player. But then the only possible conflict would be whether the player gets his Final Care or not, and at that point the fullness of his caring would reveal itself as total emptiness.
Anything valued points beyond itself, to a value. But that value, being valued, also points beyond itself; and so on. The character of value is transcendence.
So far for a philosophical backing; let's return to game design. If, as I maintain, there is no difference between task resolution and conflist resolution; if any example can only be about choosing a different level of concerns as the one on which resolution takes place; then what was the use of the distinction?
The distinction between TR and CR made people aware that there are different levels of concern on which resolution can take place. This led people to reconsider the level they were using, and finding out that often, it was not the most satisfactory level. It allowed us to see that small physical actions were not always the best level.
That is all. It was enough. It was great. But now we can put those two terms to rest, because the distinction they tried to mark does not exist.