In the orginal big diabetic study (DCCT) the measure of how much glucose had become 'stuck' to haemoglobin was detemined by the fraction of the sample that came off the croamatograph.
The third column after plain haemoglobin was the glycated one - hence the 'c' .
The measurment is clearly tied to the method of measurement, ie the gas chromatograph, if you use another method of analysis to reach make a suitable comparison you have estimate what a similar sample would have produced on the original equipment.
Intead of estimating what a chromatograph would give - the IFCC value is mmol/mol i.e. an absolute value of the proportion ( effectively a tenth of a percent). This is effectively the difference between volume and weight.
( if you have a barrel of apples how much have maggots vs how many ).
As an analogy sphygmomanometers ( blood pressure meters ) used to actually have columns of mercury the height of which was used to indicate your blood pressure. There is a standard SI unit for pressure the Pascal - Pa expressed as Newtons per square metre. In terms of blood pressure - everyone thinks in terms of mm Hg.