Four Secret Boxes exist all the time, and another appears during certain campaigns. The name and contents of the campaign box vary based on the campaign, but its keys can be obtained during the campaign, and both unused keys and the box will disappear after the end of the campaign.
The Gold Box is the only Premium box always available. This can be opened with a Gold Key or gold. Gold Keys can be obtained during quests, fairies, or certain campaigns (such as Eternal Dungeons.) When the Bonus Guage reaches 100%, it becomes the Ultimate Box. Overlap experience for the Gold Box is 50, and the Ultimate Box gives 150. The best warriors can be obtained from the Ultimate Box, and warriors with high rarity can be obtained from the Gold Box.
The Silver Box can be opened using either 100 Tokens, or for free once per day, starting at midnight Eastern. It also yields new warriors, but many of these are the lower-rarity ones. Overlap experience from the Silver Box is 10. when the bonus Guage reaches 100%, it becomes the Silver Box Plus, which gives a better chance at warriors with higher rarity and overlap experience of 50.
The King's Barracks gives 50 experience to a warrior with 5 stars of rarity or more. When the bonus gauge reaches 100% it gives 500 experience to a warrior with 5 stars of rarity or more. Costs 15,000 Silver to open. You cannot obtain new warriors from this box; only experience for warriors already owned. Additionally the King's Barracks is only available on Thursday during any given week.
The Barracks gives 10 experience to one warrior at random. When the bonus gauge reaches 100% a random warrior receives 100 experience. Costs 3000 silver to open. You cannot obtain new warriors from this box; only experience for warriors already owned.
Since you cannot have two of the same warrior, any time a box gives you one that you already own, that warrior receives Overlap Experience instead. The amount varies based on the box from which it was obtained. If the warrior is already at its maximum level, you instead receive experience books in the amount which the warrior would have received.