A TRS cable is called 'TRS' because it stands for Tip, Ring, Sleeve because of the design of the jack socket and jack plug used.   TRS cables can be used for Stereo operaton where the Tip represents the left channl, the Ring the right channel and the Sleeve is a common connection for both left and right channels.  A TRS cable can be used for a balanced signl connection as in a professional rig and in this capacity the idea of a balanced connection is to reduce excess interference or noise on long cable runs.  Stereo and Balanced do not nean the same thing.

In the context that you need to use a TRS jack plug connected to two cables into the headphone DI output from your Spider IV  The usage here is for stereo operation.

You will need one of these jack plugs at one end of the cable:

with the tip and sleeve connected to the tip and sleeve of one of the plugs below for the Left channel; and with the ring and sleeve  to the tip and sleeve of a second jack plug as shown below for the Right channel:

The use of one of these cables will mute your amp's speakers in exactly the same way as your headphones do

Nick