|The Big Model|
If you have played a role-playing game, you know that sometimes, during the game, you have to roll dice, draw cards or use another kind of Fortune mechanic to resolve something that it's in doubt: for example, if your character can hit his enemy, how much damage is inflicted, with what effect, etc.
(some role-playing games don't have Fortune mechanics, but for this example, let's consider only the ones that do)
These kind of "resolution" fortune mechanics are characterized by two different aspects: "what they do" and "when you use them".
Traditionally, in a lot of rpgs in the past the answer to the "when" question was "every time the character try to do anything that is not automatic or impossible", or more in general, "every time the character try to do something and there is concrete doubt about the results".
To be more clear: you roll when your character try to climb a wall, translate a book, find a secret door, cast a spell, hide in shadows, paint a painting. You roll (or draw cards or do what the game rules say you have to do) to know if your character is competent enough to do something, a "task".
This kind of resolution is called "Task Resolution", no matter what the resolution rules do (the answer to the "what they do" question).
Known issues and problems
This kind of resolution, being both (1) a Fortune mechanic, and (2) a measure of the character's competency, tends to devalue the character's competency. No matter how skilled the character is, he will fail a lot of times (when the failure rate become frustrating for the players it's called Whiff Factor).
Another known problem is that the result is usually in the form of a "yes he do it", or "no, he is not able to do it" result. This means that a failure simply stop the characters (and the adventure) right there, until the players find another way to do what they needed to do (this very common problem pushed a lot of Game Master to begin fudging dice rolls or difficulty levels to avoid these failures)
Both these problems are accentuated by the way Task Resolution is almost always associated with Fortune-at-the-end, making this combination absolutely unsuitable for any game that is intended to produce a coherent and dramatic narrative with competent protagonists.
Are Task Resolution and Conflict Resolution incompatible?
No. Many games present both, for different cases. Even D&D, from the first editions, had a Conflict Resolution Combat System associated to abilities used with Task Resolution.
Are Task Resolution and Conflict Resolution the only possible choices?
No. They only list two possible "triggers" for the use of a fortune mechanic (when the character try to do something, as a task, or when the character is in a conflict)
A Technique in which the Resolution mechanisms of play focus on within-game cause, in linear in-game time, in terms of whether the acting character is competent to perform a task. Contrast with Conflict resolution.