Are the two wires of a speaker identical?
No, they're not the same.

If you apply a positive voltage to the white terminal (relative to the black terminal), the speaker cone will move one way, and if the voltage is negative (making the black terminal more positive), it will move the other way. Audio signals are AC, which means that the speaker cone moves both directions from its neutral position as it operates.

The absolute polarity of the movement becomes important if you have more than one speaker, in which case, you want all of the speaker cones moving the same way at the same time. This is called "phasing", and if you get it wrong, some really strange things can happen to the sound. This applies both to multiple speakers in the same cabinet, as well as multichannel sound systems (e.g., stereo or surround-sound) with multiple cabinets.

That's why the terminals have distinctive markings.