Chest Traps are a method of protecting property. They can be applied to any container that is capable of being locked. So long as this is then opened in future using only the key, they will have no effect - The trap is enabled/disabled with the lock itself.
On the other hand, chests found in the wild seldom come with keys available, yet often have traps installed. Once the lock has been dealt with (either via Lockpicking or the Unlock spell) the trap must also be circumvented.
The usual method of doing this (assuming a trap is suspected) is to stand well back and cast Telekinesis on it, though this is not possible on the shards of Mugen or Siege Perilous. The Remove Trap skill is of course another (somewhat less safe) alternative.
Those in a hurry (or simply unaware of the danger) can always simply throw the lid back and face the consequences directly. While chests found in camps or dungeons usually aren't lethal for the well armored character, chests recovered from Paragons are more then capable of removing one's head to a location several yards from one's body.
Any given container can have multiple traps installed in it, though only one of each type.