In the past, the terms "digital amplifier" and "Class D amplifier" were often used interchangeably.
The term "Class D amplifier" has a specific meaning... although there are several variations on that theme.
It basically describes an amplifier with a "switch-mode output stage" of some sort - rather than some sort of "linear mode" output stage.
(Note that the "purely digital amplifier" I describe below does fall into this category.)
Class D amplifiers use some sort of strategy whereby they deliver a series of pulses of the same voltage level.
This series of pulses is then fed through a filter which converts them into an analog output voltage.
They then internally vary either the width or spacing of the pulses, in accordance with the input signal, which varies the energy they contain, and in turn causes the output voltage to vary.
The most common method foro doing so is PWM (pulse-width modulation).
As you might guess... with PWM the pulses are all at the same frequency and their width is varied.
There are other methods that involve varying both the spacing and the frequency of the pulses - but the result is quite similar.
With this sort of amplifier, the amplifier still accepts an analog input, and some of the internal processing is performed in the analog domain.
(Most Class D amplifiers accept an analog input signal, convert it to pulses using a triangle-wave modulator, and use analog feedback around the output stage.)
I have seen the term "digital amplifier" used to describe Class D amplifiers with digital inputs (like S/PDIF or USB).
(Usually in discussions where the author is comparing "analog amplifiers" (Class A/B) to "digital amplifiers" (Class D) ).
It is also possible to design a Class D amplifier that has a digital input and operates entirely in the digital domain.
The amplifier accepts a digital input signal, which is then processed by some sort of digital circuitry, which directly produces pulses of different widths or spacing "numerically".
I have heard of versions of this, for use in devices like cell phones and computers, delivering relatively low power, that simply don't use feedback (they are very efficient).
However, since the output required by most speakers is analog, in order to use global feedback, the output would have to be sampled using an A/D converter, in order to provide a digital feedback signal.
Although many power supplies work along these lines, I don't know if anybody is building a commercial amplifier product that works this way or not, but it is certainly possible to do so.
(It's one of those things which can be built quite simply, using a few parts, on a breadboard, but can be difficult to get to work well enough, and with low enough distortion and wide enough bandwidth, to be useful for audio applications.)
However, because "digital amplifier" is a somewhat vague term, you would need to see more technical details to determine exactly what the manufacturer means by that description...
Is there really digital amps? If it is a class D amp it is just that and not a digital amp. Of course I could be wrong.