You are correct that some manufacturers use 2 for non-inverted and some use 3.
All sound starts out being single ended in the sense that there are compressions and rarefactions in the air that can be coverted to a corresponding electrical signal with positive and negative amplitudes. There is no such thing as balanced sound waves, only balanced electrical signals.
Some time ago somebody figured out that most of the elctrical noise getting on their wires between components could be canceled if they first took the original signal (the non-inverted) and inverted it, then pass these two signals separately down the amplification chain, amplifying the difference in them as they go. The noise that was picked up by the wires will not be amplified because the system only amplifies the difference in the two lines, and the noise is the same on both lines. Very clever.
This was very handy in noisy enviroments with lots of equipment like recording studios and with wires over long distances. The drawback is that the circuitry is more complex from beginning to end since you essentially have two amplification chains for each channel, four total for stereo, that have to be perfectly balanced to get the full benefit of the noise cancellation, and it will introduce distortions if it is not.
Then a really clever fellow saw that he could make balanced equipment for the home market, market it as better because "that's what the pros use" and cash in on a gullible public even though almost nobody in a home enviroment suffers from the type of noise problems that these circuits are good for. The cable fellows were delighted because they could charge a lot more for balanced cables even though the increased cost in materials was negligible.
Stick with single ended. It's cheaper, works just as well or better in your home, and you don't have to worry about which pin is hot on your cables.