Quirk et al. (1985, A Comprehensive Grammar of the English Language) refer to "my"/"her"/"our"/etc. as possessive pronouns (see Section 6.29, p. 361). They also refer to "mine"/"hers"/"ours"/etc. as possessive pronouns. The difference is that they call the first set "determinative possessive pronouns," and the second "independent possessive pronouns."
Huddleston & Pullum (2002, The Cambridge Grammar of the English Language) call them "dependent genetives" and "independent genitives." They write, "The dependent and independent genitives are often analyzed in traditional grammar as 'possessive adjectives' and 'possessive pronouns' respectively, but we find this an unsatisfactory way of handling the difference" (p. 361).