I think the following, Warren's analysis, quoted in Kullenberg: Functions of attributive adjectives in English, explains well that there is usually a restriction involved:
Over the last four or so decades, there have been 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 is probably Warren’s
Classifying Adjectives (1984a), in which it is suggested that
premodifying adjectives may identify, classify or describe.
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
Give me the red book,
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.
Of course, a given adjective may perform different roles in different contexts.
But the terms you then go on to ask about are essentially new terms, compounds. Unlike 'Danish butter', 'peanut butter' is not a subclass of 'butter', but a related product. A new two-orthographic-word lexeme.
A partial function has different definitional requirements from a function (though hypernymy will be involved). And Wikipedia for instance states that 'In abstract algebra, a semiring is an algebraic structure similar to a ring'. As for 'market', it's a famously polysemic word, so trying to compare 'the market at Bury' with 'the stock market' is nonsensical.