Digital in the case of an amplifier does not refer to it being a "logic, or digital output" amplifier.
People use slang to describe Class D as "Digital". It is not in fact digital.
Music is analog, it is output to an amplifier as an analog signal. In a normal standard amplifier as we know it, Class AB, Class A, or Class B, the analog signal is passed to the "Audio Frequency Amplifier" (AF Amplifier) section of the amplifier, which is also called by some "the final output stage", as an analog signal, which is simply increased in amplitude (amplified) and then sent to the load (speaker).
In a class D amplifier it is different, but the beggining and END results are the same:
input goes into the amplifier as an analog signal from head unit. This signal is passing into a converter circuit that converts the sine waves (music) into a pulse which is considered to be digital, not sure if it really is though, this circuitry converts the musical input into a pulse which is used to signal the pulse width (on time) of the output transistors (mosfets) in the AF Amplifier section of the amp. Mosfets are most efficient when switched on and off quickly. Not when slowly turned on and off like transistors in a class AB, A or B, amplifier. So to optimize efficiency, the mosfets in the AF Amplifier portion of a Class D amplifier are switched on and off at a set rate usually around 1Khz in a standard non-full range class D amp, and the amount of time they stay on or off is the pulse width. The signal going from these mosfets is then passed through a filter that remove the 1Khz switching noise (square wave, sounds like a chainsaw running) and also shape the signal back into something that resembles a "Sine Wave" rather than a "Sqaure Wave" so that the output on the speaker terminals closely resembles the original input signal which is/was musical. Sine waves are musical. Digital Square waves are NOT and sound like a chainsaw running....
Trying my best to put this into "laymans" terms but it's not easy. Hope I helped you understand a little. A digital amplifier is not digital in it's output, it is analog, because your speakers MUST have an analog input signal to sound musical. The digital part is in the switching on and off conversion method that goes on inside a Class D amplifier.