Interesting question. The best account may be that in the Oxford Dictionary, where there is a helpful discussion of the differences between comprise and include.
Comprise primarily means ‘consist of’, as in the country comprises twenty states. It can also mean ‘constitute or make up a whole’, as in this single breed comprises 50 per cent of the Swiss cattle population. When this sense is used in the passive (as in the country is comprised of twenty states), it is more or less synonymous with the first sense (the country comprises twenty states). This usage is part of standard English, but the construction comprise of, as in the property comprises of bedroom, bathroom, and kitchen, is regarded as incorrect.
On the differences between comprise and include, see below:
Include has a broader meaning than comprise. In the sentence the accommodation comprises 2 bedrooms, bathroom, kitchen, and living room, the word comprise implies that there is no accommodation other than that listed. Include can be used in this way too, but it is also used in a non-restrictive way, implying that there may be other things not specifically mentioned that are part of the same category, as in the price includes a special welcome pack.
From this standpoint, which is consistent with Cambridge and Merriam Webster, comprise introduces an exhaustive list. Otherwise, use include or contain.
In passing I note that comprised of, a phrase much used by pretentious British estate agents instead of comprise, is wrong, stemming from a confusion with composed of.