Chests are found throughout the maps in the game.
Menu Chests are blue and give you access to the game menu where you can save the game, check stats and equip and use items. Example: In the top floor of the Lair.
Saving Chests are red and give you access to the saving screen. These tend to appear in situations when menu access is restricted, like if you're tied up. Example: Outside of the Mage's Tower.
These are found throughout the game and usually contain common items such as potions and perfumes. Some of these however also contain rare 1 time use items like IKO Bombs and Legendary Lamps.
Big Chests look like Menu and Saving Chests but have a wooden color. They mostly contain unique items like costumes, teaching scrolls and Key Items. These chests are often found in Bonus Areas, and sometimes as decoration in out-of-reach places.