I like to think about this in terms of "ensembles", or a distribution on the problem instances you're drawing from. NP-Hard talks about worst case in this set o

I like to think about this in terms of "ensembles", or a distribution on the problem instances you're drawing from. NP-Hard talks about worst case in this set or distribution, even if the "average" or "normal" case is creating an instance that is "easy" to solve. This is part of the problem of using technical terms in a lay context. "Hard" here talks about "worst case hard" or "provably hard" (via a reduction to 3-SAT). Whether a given instance of an NP-Complete problem that is drawn from an ensemble or distribution is "intractable" is a more subtle question.