What is the difference between bad luck and misfortune?

Pretty much they are interchangeable in use.

Bad luck is based on the belief that there is a power/force out there that can bestow or withhold the occurrence of "good things." It is also described as the events or circumstances that operate against a person.

Misfortune is a Word used to describe a hypothetical force or personified power that unpredictably determines events and issues unfavorably.