No. Because goal and approach are both essential and inseparable parts of the action. There’s no automatically succeeding on the approach but needing to roll for the goal. There is an action that is composed of both goal and approach, and if the results of that action are uncertain, one roll to resolve that uncertainty. In this particular example, the action is trying to to distract the guard by throwing a rock at a tree. That is something that could succeed or fail, with a meaningful difference between the two, so we use a roll. On a success, throwing the rock at the tree succeeds in distracting the guard. On a failure, it does not. The way I would narrate this is that the rock hits the tree, and the noise alerts the guard rather than distracting him, because that makes the failure consequential. If failure simply meant the rock missed the tree, it would not represent a change in the circumstances. Nothing would prevent the player from attempting again and again until they succeed.
Okay, I think I was a bit confused because you said hitting the tree with a thrown rock (the task/approach) is trivially easy and wouldn't require a roll. By that, I understood you to mean the task would automatically succeed, no roll required, and it does appear that you are having the rock hit the tree on both success and failure of the die roll. Likewise, you're calling for the roll to determine if the intent is accomplished, so I'm not sure what about my post you're objecting to except that I'm talking about task and intent as two things that can succeed or fail independently, which is what it looks to me like they're doing in your description of your adjudication, but after reading your post I think I was wrong about that.
What…? This is word salad to me.
What I mean by "maintain the relationship between task and intent" is that task and intent both either succeed or fail together, similar to what you're saying above. Task resolution only cares about the success or failure of the task, so you can succeed on the task but fail on the intent, or fail on the task but succeed on the intent, "breaking" the relationship between the two. I thought that's what you were describing happening in your adjudication, but I now think I was mistaken.
I don’t understand what you’re asking.
I'm asking two things or maybe the same thing in two different ways. It has to do with you having said the stone hits the tree on both success and failure. I've been calling that the task, but it's an oversimplification or shorthand for hitting the tree in such a way that would prove successful in distracting the guard, which I think has led to our miscommunication. In an earlier post, you had basically dismissed that task as trivially easy, leading me to believe you were ruling it an auto-success. My questions were an attempt to understand why then you were calling for a roll and if it was because you were subbing in a different task (hitting the tree just right, or something else) rather than the one you had said you'd let succeed automatically (just plain hitting the tree), which I now think is probably what you meant.
The player is rolling because the outcome of the action they declared is uncertain - it could reasonably succeed or fail to achieve the goal, and there’s a meaningful consequence for failure. I’d call for a Dexterity check personally, since the action involves precision and aim. If the character has a relevant proficiency (maybe deception?), the player could add their proficiency bonus.
It’s a roll to resolve the outcome of the action that was declared by the player.
I think you missed the "If not" at the beginning of my question which referred to my previous question which you don't seem to have understood. My bad for not having been more clear. From your response here, though, especially that you'd call for a Dex check, I'd say you do seem to be using the die roll to resolve whether the task (throwing the rock) is performed in such a way as to achieve the intent (distracting the guard), thus maintaining the relationship, in this ruling anyway, between task and intent. I'd say our miscommunication here highlights the difficulty of knowing what GMing principles might be in play from moment to moment that would allow a task resolution system like 5E's ability check system to possibly result in something that looks more like conflict resolution.