Audio signals are usually intended to be voltage mode. In other words, the ideal source for a audio signal has 0 Ohms, which means its voltage doesn't vary regardless of what the load does. Of course 0 Ohms is not possible in reality, but there are various levels of close enough.
Power amplifiers designed to drive speakers have very low output impedance. Speakers are usually rated at 8 Ω, so audio power amps have output impedance a fraction of that. This is done by feedback internal to the audio amp. The feedback adjusts what the final output stage does so that the voltage immediately leaving the amp is what it's supposed to be, largely not effected by the current the speaker draws. Again, 0 Ω is not possible, but good audio power amps have output impedance less than 1 Ω. It's not worth going less than a 100 mΩ or so since the wires between the amp and the speaker will add more than that.
Speakers are designed so that the sound output relfects the applied voltage, not the current they draw from that voltage. Another way of looking at this is that the speaker impedance is not a flat 8 Ω accross the frequency range, and it's not purely resistive either. If it were a purely resistive flat 8 Ω, then it wouldn't matter whether you drive it with a voltage or current signal since the two would always be proportional to each other. However, it's not a flat 8 Ω, so voltage and current aren't the same. The industry has converged on using voltage as the true audio signal, with current being whatever it ends up at roughly 8 Ω but with significant variation accross the frequency range and some reactive component. If you were to drive such a speaker with a current signal, you would get more distortion and poorer frequency response than with a voltage signal.