The IUPAC Gold Book defines
Amount of a constituent divided by the volume of the mixture. Also called amount-of-substance concentration, substance concentration (in clinical chemistry) and in older literature molarity. For entities B it is often denoted by B. The common unit is mole per cubic decimetre or mole per litre sometimes denoted by M.
Number of entities of a constituent in a mixture divided by the volume of the mixture.
I can't see a distinction between the two terms since it seems to me that "Amount of a constituent" is the same as "Number of entities of a constituent".
Could you please explain the difference between them? Is it a conceptual difference or just a difference in the context in which they are most commonly used?