Wikipedia defines determiner / determinative (the POS, not the grammatical relation) in largely semantic terms:
A determiner, also called determinative (abbreviated DET), is a word,
phrase, or affix that occurs together with a noun or noun phrase and
serves to express the reference of that noun or noun phrase in the
A clear-cut example of what 'in the context' might imply is
"Pass me that book, please." [pointing to one]
Obviously, nothing about inherent properties of the book (weight, colour of binding, value, readability, genre ...) is being specified – merely its position in the environment in relation to the speaker's index finger. Its reference in the relevant context.
"That book is heavy", on the other hand, is giving an inherent attribute of the book by using 'heavy'. This is an adjectival usage.
But there are grey areas.
"Pass me the red / smaller / largest book."
use 'red' / 'smaller' / 'largest' as identifiers within the context of all the books in sight. ('Polar' in 'polar bears' is a classifier, 'red' in 'Her car is red' is a descriptor.) Though this overlaps with determiner usage, it's still reckoned that 'red', as it uses an inherent property of the object to identify it, is an adjective here.
"He is a mere youth."
uses 'mere' as a descriptor of the whole class to which 'he' belongs: immature, physically not yet at their prime, not ready for great responsibility.... It describes the context, but behaves adjectivally, giving attributes largely found in the whole group. It has been called a 'non-semantically-predicative adjective'.