The way I explain it is;
In true stereo, there are 2 channels of output, the audio to each ear can be different depending on the mix, i.e. music.
The output of a detector has 1 channel of output (mono). In the instance of 1 speaker the output goes to that 1 speaker. In the instance of headphones or earbuds, that 1 channel of output is split equally between the left and right ear and is not true stereo. It is purely the way it is wired.
The primary reason for the different wiring in metal detectors, in particular the GPX series, is that stereo wiring i.e. headphones, will not trigger the audio amp within the GPX battery box. Whereas, mono wiring will trigger the amp i.e. speaker/s.
The output of a SDC has no switchable amplifier. Plug in headphones and you get a mono response to each ear. Plug in a speaker and the output is still mono, but barely audible due to the lack of audio amplification. In other words, not enough juice to drive a speaker. Hence the reason, those that use speakers on the SDC, run one with a built in battery operated amplifier, B&Z or other booster and indeed the Steel Phase SP01.
I have a B&Z I used to run on the 5000, I tried it on the SDC, getting a background hum and "crappy" result. Which is why after borrowing a mates SP01, I bought my own.
I'm confident that Pat will agree, wether phones are stereo or mono will make no difference with the SP01 other than which mode switch you use. What may make the difference is the impedance of the phones, notwithstanding quality.
I've tried earbuds, the Koss GPX phones, SDC Koss phones and the Deteknix wireless. With my hearing, I can't discern enough difference to matter. So to allow me not to be connected by wire to the SDC, I stick with wireless. BTW my patch leads are all mono wired, as I don't want to trigger the 5000 amp if using the SP01 with the GPX.