This is subjective, and I'm not sure whether true, or not -but to me, "ache" lasts much longer, than does pain. But then, we do say - I was in such pain (following an operation, for example) and NOT I was in such ache...
I felt a sharp pain, but a dull ache...good question, wish I had an answer :-)

see post #4 in this thread Siehe auch: pain or ache
for a good explanation

Hey, I wasn't that far off the mark :-)

I think of "pain" as much more intense than "ache". When something aches, it hurts a bit but you can live with it. Pain, on the other hand can be quite excruciating and you often only a prescription painkiller will help it.

I'd say that an ache is always "dull", whereas pain can be "dull" or "sharp" (in addition to the already-mentioned fact that an ache is something long-lasting).

and my tuppence worth (leaving aside the figurative pain of parting and heartache):

"Pain" is an unpleasant sensation resulting from the stimulation of specialized nerve endings. It may be acute or chronic; mild (discomfort), moderate (distressful) or severe (agony) in intensity; dull, sharp, stabbing, lancing, throbbing, colicky etc. in nature; brief, sustained, constant, recurrent in timing.

An ache is just one type of pain - generally dull and sustained, fixed rather than in twinges, usually mild/moderate but may also be severe.