It is best to start by examining the semantic (/ pragmatic) roles of adjectives. Those in the attributive position manifest the fullest range. A paper by Helena Kullenberg [slightly modified below] examines Warren's 1984 analysis:
[During the 1960s - 90s], there [were] sporadic attempts at accounting
for functions of attributive adjectives (Eg Teyssier 1968, Bache
1978, Warren 1984a, 1984b, Halliday 1994). One of the most thorough
and exhaustive studies presented so far [was] probably Warren’s
Classifying Adjectives (1984a), in which it is suggested that
premodifying adjectives may identify, classify or
Classifiers and identifiers are claimed to differ from descriptors in
that they somehow restrict the range of the head noun; the former
restrict semantic range, pointing to a subcategory, and the latter
restrict reference, indicating a certain referent or group of
referents within the class denoted by the noun.
An example of a typical classifier is polar in
- I saw some polar bears at the zoo, where polar indicates a subcategory within the class of bears.
An example of a typical identifier is red in
where red ’picks out’ the intended referent from the class of books
(or rather, from a contextually determined set of books).
Descriptors, on the other hand, are seen as optional elements adding extra, nonrestrictive information.
An example of a typical descriptor is cuddly in
- I saw some cuddly teddies,
where the adjective simply adds descriptive information about the
teddies in question.
Looking at predicative usages, we see that 'That bear is polar' / 'The reaction is chemical' are not available. Classifier usages must (normally) be attributive.
'The angry man' may be either an identifier or descriptor usage.
As an identifier, it doesn't make sense to have a basic 'The man is angry.' A paraphrase using a defining relative clause such as
'The angry man is the one we suspect.' ↔ 'We suspect the man who is angry.'
As a descriptor,
'The angry man soon left' ↔ 'The man, who was angry, soon left' are paraphrases. And 'The man was / is angry' is available here as a simple statement of fact.