I think they are connected. It's possible that Fierce Deity and Majora were once bitter rivals. Because of this, they had a huge fight. When Majora had almost been defeated, realizing that he could not defeat Fierce Deity, he sealed his soul inside a mask (Majora's Mask, obviously). Fierce Deity, seeing that the mask would cause terrible danger in the future, also sealed himself within a mask (Fierce Deity's Mask) so that if Majora's Mask did cause destruction, his mask would be there to defeat him. Also, when Majora Kid gives Link Fierce Deity's Mask, he does it so that "it can be a true game of bad guys versus good guys." This is another hint that supports this theory.