This is a linkpost for https://dkl9.net/essays/will_issue.html
Another way to operationalize this difference you called out at the end is by saying, counterfactually if I were sufficiently motivated to do X, I would do it. Of course this leads you just as dense a philosophical thicket, just moving it to the nature of counterfactuals rather than the nature of will.
But in some ways your conception of the problem is also too narrow because it seems to partly include a distinction between muscle skills and cognitive skills? I am not "able" to beat Magnus Carlson at chess but it isn't because I'm physically unable to move the pieces appropriately.
This post contains content that might be regarded as spoilers for the free will problem
I cannot jump off a cliff. I do not know any cliffs near me, but that's not the reason I care about, so we'll counterfactually skip over that. The more interesting reason I can't jump off a cliff is that I don't want to. When we confidently know that I don't want to jump off a cliff, and that no one in the near future would coerce or manipulate me to, we can conclude a negligibly tiny probability for my jumping off a cliff, or, in practice, that I will not do that. Once we accept that "could" expresses an option's plausibility, we're saying that "it cannot happen that I'd jump off a cliff", and, equivalently, "I couldn't jump off a cliff".
There is a straightforward sequence of muscle commands from my brain to my legs that would lead me to jump. But the existence of such motor outputs is not what we typically mean by "ability". If there was a cliff near me, but I didn't know about it (probably true anyway), that pattern of leg movements would just as much exist, but I'd be unable (in the conventional sense, not just "my" "weird" sense) to go to it and jump.
Not wanting to do something inhibits the person from doing it just as effectively as an explicit "inability". You can't just object "but free will!" (and be correct), both sith I just anticipated it, and so you wouldn't want to (unless you're trying to be annoying), and sith human minds are not mystically unpredictable blobs of chaos. People's minds have a theoretically-measurable internal state that constrains what they do.
If someone (honestly, after thorough thought, and not opposing their established habit) resolves to not do something (nontrivial and easily avoided), they will tend to not do it, unless they are affected by (sufficiently convincing) new input. A failure to accurately constrain someone's future actions is a matter of your limited knowledge about what they think or will encounter, not their inscrutable freedom to do whatever they know how, even when it arbitrarily contradicts any or all of their preferences.
Remarking on someone's intent, then saying "but they could do otherwise!" shows your uncertainty about that person's plans or future inputs, not any fundamental nondeterminism in human behaviour. Or it may show your failure to neglect small probabilities for practical purposes. If you ask me to recite ten digits of pi starting at position 1000 (I only know the first 70), I would either refuse or arbitrarily guess. The "observation" that "you could get them right!" tempts me to remind you just how small a probability of 10-10 is.
But why all the crabs?
We can tell apart will-or-skill issues, together, from non-"issues", by evaluating whether we expect a person to take a particular action.
Knowing the muscle commands needed for an action is not necessary for being "able" to do it, so it can't be how we distinguish will issues from skill issues. If a (reasonably large) target is to appear at a spot yet to be determined near me, I'm "able" to throw a ball and hit it, but I do not know the exact movements needed until I actually do it, and cannot know until I see the target.
Knowing a verbal procedure for an action is not sufficient for being "able" to do it, so that can't reliably distinguish will from skill, either. If you read about how to ride a bicycle, but have never tried it, you'd recite the procedure when asked, but not be able to actually do it.
There is no straightforward measurement to distinguish will issues from skill issues as they happen, as far as I can tell (tho if you know one, I'd like to hear it). Yet by merging the cases into the description of "can't do that", I seem to be striking terms from expressive vocabulary. If we speak of these things differently, we expect that there's a real difference between them: what is that?
The difference lies in how you respond to the "issue". Leading someone to do something, when you expected at the start that they wouldn't do it, usually takes one of two forms. If it's done by teaching, or by giving resources, we regard the limitation that existed without that intervention as a skill issue. If it's changed by argument or incentives, we think of it as a will issue. Statements that someone "could" do something mean that you'd get the person to do that something by arguing to or incentivising them, and you don't need to teach them or give them new resources.