아빠 and 아버지 mean father or dad. In Korea, children, young and old girls usually call father as "아빠" . Because they make themselves delightful to father in Korea, their father receive their charms. Do you know the difference "엄마" between "어머니", "형" between "형님", "누나" between "누님" and so on? It is same meanings.

It is same meaning. But when you call your father yourself, you can say 아빠 Otherwise, if you say your father to another person, like when you talk with your friends or when you are in public place, you have to say 아버지 Here is summary, except when you call your father directly or talk about your dad among your family members, we usually say 아버지

Dad = 아빠 Father = 아버지