What specifically does PCM refer to?
I like this paper a lot: The philosophy of PCM. It explains PCM very clearly, includes references to some of the earliest papers on it, and you can hardly argue with the qualifications of the authors :)
PCM was conceived as a three-step process. First, sampling (at frequency $f_s$ sufficiently above Nyquist). Second, quantizing (with enough resolution $\Delta$ to obtain the required quantization SNR). Third, coding, or mapping the quantized samples to $M=2^k$ pulse amplitudes, with $M$ chosen to obtain the required line pulse rate.
PCM, then, has parameters $f_s$, $\Delta$ and $M$. Each of these affect system performance in different ways.
Why use the term &quot;modulation&quot;? In communications, &quot;modulation&quot; is very general, and is used almost as a synonym to &quot;mapping&quot; or &quot;converting elements from an input set to an output set&quot;. In fact, what you understand as &quot;modulation&quot; (multiplying by a carrier) is often called &quot;upconversion&quot; and &quot;downconversion&quot;, to avoid confusion.