Generally speaking, balanced and differential signaling are two different things. They’re often (but not always) used together, and in audio, the term “balanced” refers to this.
Speakers and Headphones
A speaker or headphone responds to the voltage difference between its 2 input wires. It doesn’t assume either is ground, though one might be, it doesn’t matter. So connecting a speaker or headphone to a balanced output is easy. Just wire (-) to (-) and (+) to (+) whether or not the (-) is a ground (unbalanced output) or carries a signal (balanced output). If the unbalanced output has a common ground for both channels (like a headphone), you can split it to both L and R (-) in parallel.
Converting a balanced speaker or headphone output to an unbalanced connector is not as simple. An unbalanced headphone cable (a standard 1/4″ or 1/8″) has 3 wires: L (+), R (+), and a single wire that is a common ground for the L and R. You can’t connect a balanced output’s (-) wires to this ground. That would mix the channels, and allow the amp’s output stages to drive each other, which is bad because they usually have very low output impedance, so it can overdrive the output stages. Also, you can’t just ignore the output’s (-) wires and connect the headphone (-) wires together; this will give a common floating ground. In short, you need a transformer to do this conversion.
If the balanced/unbalanced conversion is between components like a preamp (not a speaker or headphone), it gets more complex because unbalanced components assume the (-) is a ground, but the balanced (-) carries a signal and its ground is a separate (3rd) wire. You can’t connect a balanced output (-) signal to ground; it will overdrive the balanced output as it tries to swing a voltage over a 0 ohm load. Also, you need to ensure the (-) wire has the same impedance to ground as the (+) wire.
So the best way to convert unbalanced to balanced between components is to use a transformer.
However, you can wire unbalanced output directly to balanced input. Connect the unbalanced (-) output to both pins 1 and 3 on the balanced side (negative & ground), and the unbalanced (+) output to pin 2 on the balanced side (positive). That is, carry the unbalanced source ground through to the balanced input. Since unbalanced (consumer) output is at a lower voltage than balanced (pro), the downstream balanced component will be receiving a lower level signal than it expects. This may or may not be a problem, depending on how clean is the input signal and the balanced device’s input voltage sensitivity and gain.