It's a really good question. You gave me food for thought. lol Anyway, 채굴하다 and 채광하다, thoes two verbs have literally the same meaing as mining in English. But, I reckon 채굴하다 is more commonly used for mining coal. And the verb, 채취하다 has widely used in collecting something or extracting something. For example, we use that word in some sentences like 지문을 채취하다 (taking somebody's fingerprints) or 혈액샘플을 채취하다 (taking a blood sample). Originally, the letter '채' is the root meaning of those three word as collecting something. Hope this explanation will help. Thank you.