I pretty much think that if the person can't hear the same as hearing people can, they're hard of hearing. If they can't hear anything at all without hearing aids or an implant, they're deaf.
Those are how I define the words in the physical sense. That said, I know people who are hard of hearing by my definitions and use the label 'deaf' for themselves. I know people who are deaf by my definitions and use the label 'hard of hearing', so while that's usually how I would define the terms, not everyone will agree with me, and different people have different tastes with regards to which label they like more.
