명절 명절 means traditional holidays. But only 설(new year in lunar calendar) and 추석(August 15th in lunar canlendar) are designated as legal national holidays. There are more 명절 which Koreans celebrated in the past, but they are fading away except those two. 휴일 휴일 means holidays, or closing days when used with context of business. 휴일 literally means "days to rest". 공휴일 공휴일 literally means public holidays. Both of two 명절 are public holidays, so they can be considered as 공휴일. And there are some more public holidays like 3.1(The independence day of Korea), 5.5(Children's day), and so on.