Though both words gives negative vibes or can say unpleasant sensations that one feel in one’s body,but there is a slight difference while using them.
Ache is used when there is a continuous discomfort in a particular part of body.It is a part of pain.It is not as acute as pain.
However,pain is a broader term.It can be physical,emotional of mental discomfort which is difficult to ignore.It is usually stronger and more sudden.
For instance;I have a backache from last five years.
It means you have a continuous backache and is tolerable.
After hit by a car,I felt a sharp pain in my back.
It means a lot of intolerable short term pain in my back which can be cured by the medicines.