Your top circuit shows the input signal has a positive polarity so a polarized capacitor can be used.
Your bottom circuit shows that both inputs have the same polarity and voltage so no capacitor is needed.
Your bottom circuit shows a high frequency to the top wire of the speaker and a low frequency to the bottom wire of the speaker. It reduces the total power or requires 2 power amplifiers to do that. You could use just one power amplifier to drive one wire of the speaker if the signals are mixed together ahead of the amplifier.