Alright! Well...
...I believe that the 'Fierce Deity' was once one of the commanding soldiers in King Igos du Ikana's army. He looked like Link from Hyrule, and they shared the same name, but his personality was different, but in some ways similar. This Link loved battle and war, and while the Hyrulian Link may like to fight, it's mainly to protect something. The Terminian Link just loved fighting, no matter the cause.
It was through this lust for battle that the Terminian Link got his nickname, the 'Fierce Deity'. One of the finest warriors in all of Termina, his aggressive attitude made him 'Fierce' and his skill in fighting made him like a 'Deity'...none could best him in combat. Until...
One day, Majora's Mask was released from its prison (As you put it) in the Stone Tower Temple. It immediately proceeded to wreck havoc on Ikana, and so King Igos du Ikana ordered his finest soldier, Link, to command the King's army and destroy it before all of Termina was wiped out.
Against Majora's overwhelming power, most of the regular soldiers were destroyed. The Terminian Link may have been arrogant and a little selfish, but like any good Deity, he cared about his own. He ordered the soldiers to retreat, and challenged Majora's Mask to a one-on-one duel, during which he was beaten and almost killed.
Majora thought of this man as evil, a 'bad guy', for sending so many soldiers to their deaths. Instead of just simply killing him, it trapped his spirit into a Mask and kept it until that fateful day inside the Moon.
After gaining Fierce Deity's Mask, the Link we all know and love wore it against his final battle with Majora. Immediately, he felt a surge of power and memories as the Terminian Link's soul 'fused' with the Hyrulian Link's, created a perfect being of almost unstoppable power. The Hryulian Link's desire to protect Termina, and his skill, combined with the Terminian Link's strength and desire to fight, proved to be too much for even Majora's full Wrath.
In the aftermath of the fight, when the Moon was being sent back to its rightful place in the sky (Or being destroyed, depending on what you think...), the Fierce Deity had had his revenge against the beast who had trapped his soul for many years inside a mask. Through this, he was able to free himself from the mask and rest in peace. So ends the story of the Fierce Deity.
I guess that's not what you were expecting, right?
Well, it's more of a fan fiction than a theory, but I was trying to come up with reasons why the Mask is 'Fierce Deity's', why the Mask looks a little like Adult Link's face and why the Majora's Mask wearing kid inside of the Moon says that you'll be the 'ultimate bad guy' when you wear the mask, and this is what I came up with.