OK. So, you are making a difference between spectral counting and intensities (incl LFQ)? Up to now, we mostly handled only proteomics data from LS MS/MS as intensities (or LFQ intensities).
Yes, for discrete distributions, the logCPM normalizes the sum of the counts to a million, then takes the logarithm. On continuous signals, like the intensities, "logCPM" would scale the intensities to "million intensity units", then take the logarithm, which is equivalent to taking the logarithm and shifting all values with some constant. Maybe it would be better to call it logPMI ("log per million intensity") but the calculation would still be the same.
Are you having doubt on the "CPM" step, or the "logarithm" step for continous intensities?
Ivo