Pockets, Inventories and Lighthouses contain different purities of Suspendium. Rachel's chair might also contain a certain purity of Suspendium so she can manipulate it, to move in the direction she wants it to.
The presence of Suspendium allows an item to float but doesn't allow it to move; moving an item is probably achieved through Shinsoo manipulation or some item mechanism. Items with minimal purity of Suspendium are incapable of floating by themselves; a user must manipulate Shinsoo so the item can float. This means the very presence of Suspendium allows an item to be able to float (by Shinsoo manipulation or by itself). Items with higher purities of Suspendium are harder to control and require a skilled Shinsoo user.
It's possible heavier and larger items require greater amounts of Suspendium with higher purity are required to make it float. Except items like the Opera and possibly Eyes of God, all objects which are capable of floating (without Shinsoo manipulation) are smaller and lighter. Examples are: Arms Inventory, Pocket, etc.
Other examples can be found in the vehicles throughout the Tower. A Suspendship is an aircraft with Suspendium in it, allowing the user to fly. Another example of this is in the crafts used in the 28th Floor by Team Tangsooyook. On the 21st Floor, Team Tangsooyook also boarded a large hovercraft.
The name Suspendium is a translated version and the Korean name given for this material would not be able to properly translate into English.