Difference between Korean language and Korean language in Korean
한국어·한국말
한국어Korean language
한국어 means the Korean language. You use it when you talk about studying, speaking, reading, or writing Korean. In school, people often say they learn 한국어 in class or practice it with friends.
한국말Korean language
한국말 means the Korean language. You use it when talking about speaking, learning, hearing, or using Korean at school and in daily life. It is a common, easy word for the language people speak in Korea.
The difference
한국어 and 한국말 both mean the Korean language. 한국어 sounds a little more formal and is common in class, books, and official situations.