Theoretically, the action can take place anywhere around the listener. True quad works only for non-broadcast audio. Broadcast quad is matrixed, not true - that is, there are only three channels, two in front of the listener and one in back. The third and fourth speakers on the listener's receiver play back the same signal, doctored to sound like two discrete channels. Matrixed quad renders the two back channels useless except for environmental overtones.
Binaural captures sound on two channels in a way that imitates human ears.
The mikes react to sound resonating in the shell like ears reacting to sound resonating through the skull. Listening with earphones, the audience can discern not only left and right, forward and back, but up and down. Over speakers, everything sounds distant, unless you compensate in the mix, which compromises the binaural effect. Used with restraint, the ability to place the listener in the center of the action has immense possibilities. However, these are the same possibilities of mono, in which listeners put themselves in the center of the action by force of imagination rather than of technology, a far superior system in my opinion.