زبانکده

how should I have to recognize the usage of them?

You can say feet sore and even feet ache, nothing odds with that. It is just a matter of degree of pain.
You may experience feet sore by simply and ordinary activity, for example standing, walking, or running, but it is just a discomfort feeling which you can continue standing, walking, or running.
You can say feet ache if you thing your feet is really wrong so you stop standing, walking, or running, but an hour later you are totally fine.
If the feet ache goes day and night where you hardly stand, walk, or run and threat your job performance, your activities, and almost everything, you may say it as a foot pain.
Regarding time, sore-ache-pain can also be categorized as an acute and chronic matter