What's the difference between 이슬비 and 가랑비?

ANSWER: Koreans say that 이슬비 is rain that means "Stay (있으라)!" and 가랑비 is rain that means "Go (가라)!" Even though 이슬비 and 가랑비 can both be translated in English as "drizzle," Koreans think of 이슬비 as "a light drizzle," like "dewdrops" (이슬), and 가랑비 as "a heavy drizzle," which would mean that "a light drizzle" tells someone to stay, and "a heavy drizzle" tells someone to go. That would make sense only if "a heavy drizzle" is a sign that "a heavy rain (큰비)" is coming and that one should get home before it starts. The only drizzle lighter than 이슬비 would be 안개비 (misty drizzle).

When you are visiting a Korean's home and it starts to drizzle, if the host describes the drizzle as 가랑비, then he or she might be suggesting that you go (가라), but if the host describes it as "이슬비," then he or she might be suggesting that you to stay (있으라) longer. Or the host might not be suggesting anything at all. Jokingly, you could ask, "'가랑비'? Are you telling me to go?"

By the way, 보슬비 can also be translated as "drizzle" but seems to refer to "a quiet, gentle drizzle," one that comes without any wind.