Both can be a blanket, but the term, "이불" is usually used for sleeping, on the other hand, "담요" can be used when sleeping, being in an airplane, when camping, etc to keep ourself warm. :) \^o^/

담요 is a type of 이불, we say 담요 이불. 이불 is blanket (duvet) and there are many types of 이불. It varies widely depending on the type of materials used and the process. I believe!