|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 tries to do anything that is not automatic or impossible", or more in general, "every time the character tries to do something and there is concrete doubt about the results." All that is Task Resolution. More recently this kind of resolution was substituted by mechanics that are used only when the character is in a conflict with someone or something (Conflict Resolution)
There are really a lot of very different resolution mechanics that are of the "Conflict Resolution" kind. When you say that a roll is "conflict resolution", all you are saying is that you do that roll only during a conflict. What that roll DO, how it's done, how it interact with the fictional content, etc change from game to game.
As such, there is no "Conflict Resolution" technique: every game with conflict resolution has specific techniques, and it's possible to consider the effect and results of a specific Conflict Resolution technique, not of "conflict resolution" in general.
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 mechanisms of play focus on conflicts of interest, rather than on the component tasks within that conflict. When using this Technique, inanimate objects are conceived to have "interests" at odds with the character, if necessary. Contrast with Task resolution.