My Own Defintions
Everybody is applying their own twist to the two terms, and I am guilty of the same thing. This next section I am offering my own take on these two terms. Note also I am not going to compare one against the other, or apply some sort of sliding scale (i.e. as you more away from musical, it becomes accurate or vice versa).
My Take On Accurate
Accuracy in physics differs from the audiophile definition. Audiophile version of accurate borrows from the physics world, but with a twist - there is no valid reference.
In Physics, accuracy is defined as error of measured value versus the true value. This true value is what we call the reference. This is an excellent XKCD comic in so many ways:
In this example the reference is 130, so 129 is not far off. Given a known reference (true value) of 130, we know 129 is approximately 0.75% off (so about 99% accurate when compared to the reference). In most typical measuring instruments, we often see a qualification e.g. +/- 10%. This metric is the degree of accuracy. The lower the number, the higher the accuracy.
Using the XKCD analogy, accuracy is now about how good your car’s speedometer is at replicating the readout of the radar gun at the same time. The better your speedo can track with the speed gun, the more accurate your speedometer is.
In the case of a CD, it is like a speed gun taking 44100 speed readings a second. Now your your sound system is like a speedometer diligently displaying the speeds at that same pace, the closer it matches the readout of the speed gun, the more accuracy it gets. This is akin to focusing on the speedometer while driving and totally miss the dangerous hazards on the road.
For me it is important to not expand accuracy to include everything- as an example accuracy in recreating the human voice does not necessarily imply it will be accurate in recreating the Cello.
People relying on measures to provide their idea of accuracy may prefer a “null test". This involves comparing the “original input” - aka the source material (e.g. a CD) against some measured output. Invert one and apply it to the other to get a result. In a perfect world the two waveforms would completely cancel each other out and thus result we obtain is 0s all around (flat line).
A variant of this idea is now championed by the measuring audiophiles - a flat 20 Hz to 20 kHz response. The flatter the curve, the more accurate the sound system is.
Or is it? It depends on who you ask, and what accuracy you’re looking for. Accuracy without reference is pointless, personally I like to term accuracy in terms of realism in recreating voices, instruments, ambiance, etc. For me it is important to tie accuracy to a known source - accurate of or to what. It all boils down to the idea of accuracy you’re interested in - accuracy to audio, or accuracy to measuring instrument.