I have tried to answer the question thus...
Pain is what the body experiences...suffering is the mentally created agony beyond actual pain (if any pain). Have you ever heard the phrase, "don't look or it will hurt more?" That hurting more is suffering...the hurting before you look is pain.
With Awakening, suffering vanishes because we are no longer mentally creating agony for ourselves. Pain, on the other hand, still exists because we have a body with nerves that experiences pain.
What do you think? How have you answered this question?