It is almost impossible to explain the difference to "the man in the street". Also, have you ever tried to explain the difference between "heat" and "temperature" to the average man in the street? Or "weight" vs "mass"?
I once made the mistake of remarking casually that walking on hot coals is facilitated by the fact that hot charcoal, while at a high temperature, contains very little heat [implication: as compared to the specific heat capacity of water in your feet]. Everyone around me smirked and said "Did you hear what nonsense you just said? Very hot but has little heat?"
I gave up after ten minutes of trying to explain the difference.