I've found myself doing some research to ascert the differences when trying to assess the colour of a given sample.
I've found two main options, which are (1) a colorimeter and (2) a spectrometer.
So far I've concluded that the main differences between both methods are: The spectrometer is able to capture wavelengths that are reflected from the sample, whereas the colorimeter is limited to specific colours (like when using an RGB sensor). This difference makes spectrometers more complex in their design and thus more expensive. This information I've taken from here.
The above picture, comes from that same source 1.
I'm wondering if the light source depicted has to meet some specific requirements, or it doesn't really matter much and a calibration under that same light source with a sample of known colour would suffice.
Source 1: Application Note - Insight on Color Colorimeters Versus Spectrophotometers - Vol. 6, No. 5 - HunterLab (2008)