Possessive pronouns as a general term

Question

Can the term 'possessive pronouns' be used as a general term for both possessive pronouns and possessive adjectives?

At the university I was taught that there are two kinds of possessive pronouns: possessive pronouns adjectives and possessive pronouns nouns. In most today's textbooks they are called possessive adjectives (e.g. my, his, their) and possessive pronouns (e.g. mine, his, theirs) respectively. (I was also taught that a possessive pronoun is an 'absolute' form of a possessive adjective.)

Update: ("Possessive determiner" – Wikipedia)

The words my, your, etc. are sometimes classified, along with mine, yours etc., as possessive pronouns or genitive pronouns, since they are the possessive (or genitive) forms of the ordinary personal pronouns I, you etc. However, unlike most other pronouns, they do not behave grammatically as stand-alone nouns, but instead qualify another noun – as in my book (contrasted with that's mine, for example, where mine substitutes for a complete noun phrase such as my book). For this reason, other authors restrict the term "possessive pronoun" to the group of words mine, yours etc. that substitute directly for a noun or noun phrase.

Some authors who classify both sets of words as "possessive pronouns" or "genitive pronouns" apply the terms dependent/independent or weak/strong to refer, respectively, to my, your, etc. and mine, yours, etc. For example, under this scheme, my is termed a dependent possessive pronoun and mine an independent possessive pronoun.

Answer 1

Yes, my, his, their etc. can be called possessive pronouns.

The rationale as I understand it is that words like "her" and "his" can stand for phrases like "Alice's" and "Bob's".

Usually, "Alice's" and "Bob's" are classified as (inflected forms of) nouns (or noun phrases). Even though they act more like adjectives or "determiners", in mainstream analyses of English grammar, inflection is not thought to change the part of speech of a word. (Analogously, the mainstream analyses of "gerunds" and "participles" classify these as verb forms, not as nouns and adjectives, even though we might expect gerunds to be classified as nouns and participles as adjectives on the basis of their distribution.)

This means "her" and "his" can take the place of nouns/noun phrases, which is characteristic of pronouns.

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As Andrew says, linguists who recognize "determiners" or "determinatives" as a part of speech distinct from "adjectives" will classify my, his, their etc. as determiners/determinatives rather than as adjectives. You can see that they fill the same "slot" in the noun phrase as the definite article the (we cannot combine the two: *"the my book is good", and we cannot leave both out: *"book is good") and not the same slot as an ordinary adjective like "red" (which can be combined in any way with either "the" or my": we can say "the red book", "my red book", "the book", "my book").

Answer 2

Personal Pronouns, Possessive Pronouns and Possessive Determiners

You are correct and there is a distinction in the terminology used to define possessive determiners (my, your, his, her, etc.) and possessive pronouns (mine, yours, his, hers, etc.).

What you were taught may not be wrong, but one thing I've learned from being on this site is that even professional linguists can disagree about what part of speech a particular word might be, and the terminology they use is constantly evolving. Apparently now these are considered determiners and not adjectives, although I'll leave it to someone with more scholarship to explain why.