From my knowledge,almost every province has their own unique dialect. Perhaps the most known is the Busan dialect, as it has unique sentence endings which people like to imitate. If you have ever watched the dramas Reply 1997 of Shut Up Flower Boy Band, you would have heard the Busan dialect. Jeju island also deserves a mention as some words are entirely different and Seoul Koreans often get confused when talking to someone from Jeju. Try googling the dialects to read about more ^^

As far as I know we have '표준말, stand Korean words', like BBC English in the UK. It is the words used by 'common people living in Seoul - 중류 사회에서 쓰는 서울말'. There are 6 major dialects and accents according to the provinces in South Korea and they are '경기도(Gyeonggi-do), 충청도(Chungcheongnam-do and Chungcheongbuk-do) 전라도(Jeollanam-do and Jeollabuk-do) 강원도(Gangwon-do) 경상도(Gyeongsangnam-do and Gyeongsangbuk-do). and 제주도(Jeju-do). Korea is relatively quite a small country but there are some ranges of high mountains that prevented people from going somewhere easily, so there are little bit of differences of using words referring same things. However, usually we have no problem having conversation between people from any province of Korea, include both South and North.