I'm not into modals, but I think both can and could denote physical capability. I can lift this box. I could lift this box. (with or without implied conditions)
With polite questions people often don't say what they mean, because they don't want to put the person addressed in a bind. If you really want to know if the person will come, Ask him. "Will you come to my party?" That covers both willingness and capability.
I'd say "could" is less committal than "can," perhaps because of it's possible implied conditions, It's easier to say "No" without offending the questioner. I agree that between the two, if the questioner wishes to address capability, he should use "can." But without any additional context to suggest that's their intention, most questioners would use "can" and "could" interchangeably. It depends a lot on the habits of the person asking, and on the social nature of the situation. "Could" is more polite; "can" is more direct. And some people are more direct by nature.
If there had been a previous conversation in which the invited person suggested he might have a conflict (Implying, perhaps falsely, that he'd be willing if he could clear the conflict), then the questioner would subsequently use "can" to reinvite him.
Many people will say "Can you pass me the salt?" You wouldn't hear it at a White House white-tie-and-tails dinner, except possibly by George himself. But no one under any conditions would take it to mean, "Are you capable of passing me the salt?"
Probably that doesn't help you at all.
- A.