Pain is a general term, whilst ache is a subset of pain - it's more specific. An ache tends to be a dull, throbbing type of pain.

Difference of pain and ache in meaning: 1- He has a deep pain in his heart since she abandoned him. 2- I'm into going for a check up, I feel a pain in my head. 3- I have headache "pain" has more general meaning but "ache" only belongs to diseases. Structural differences of pain and ache: - we say "painful" but we don't say "acheful" - we say "headache" but we don't say "headpain"