Ache lasts longer but hurts less. Pain is more short term but ‘pains’ more!
So when you run 10 kilometers and come back, the sensation you feel in your legs is the ache while if you eat street food and catch a stomach infection you may feel pain in your stomach.
When you don’t sleep for two days straight, you get a headache but if you bang your head against a wall, you get a pain in the head.