The difference is actually much more than that. As you know, in Korea they have their own way of counting age that makes people a year or two older depending on their date of birth and the time of the year. They use 살 for this one.
Now when it comes to legal age, the one that we are used to using everywhere else in the world, they use 세. So when it comes to laws, they use 세. the drinking age is 19세, 19 international age. 19살 could include 17 or 18 year olds in international age, 세 age.