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“balanced” is a dangerous word that is typically mis-used.
A cable carrying a “fully balanced” signal has a differential signal (meaning that there are two signals and a ground, and the two signals are opposite in polarity) AND their termination impedances are identical.
It is possible to have a balanced connection that does not have a differential signal. You do this by putting a resistor between ground and the wire that would normally carry the “negative” signal (XLR pin 3, for example). The resistor must be identical to the output impedance of the circuit driving the “positive” signal.
This ensures that the interference noise that is received at the other end of the cable is identical, and therefore if the input connection is balanced, the noise will be subtracted from itself, thus cancelling. This is independent of the signal. Driving the cable with as differential signal will increase the SNR by 6 dB (because of the doubling of the signal) but this is optional in an impedance balanced signal.
For example, if you look at the outputs of the original Mackie mixers, the XLR main outputs are fully balanced. (impedance matched WITH a differential signal) but the 1/4″ outputs are impedance balances without a differential signal.