There are four types of pronouns: subject, object, possessive, and demonstrative.
Our and
ours both answer the question
Whose? which, by definition, makes them possessive pronouns in form. As for their function,
our has an adjectival function (also referred to as determiner function in the literature) because it modifies nouns, whereas
ours, a pronoun that sits in a subject or object position, has a nominal function.
In short,
our is possessive pronoun in form and an adjective or determiner, depending on the terminology you subscribe to, in function. The terminology here can indeed be confusing, if you're talking about form alone:
our form:
possessive pronoun ours form: possessive pronoun
The terminology is not confusing, however, if you're talking about function:
our function: possessive adjective ours function: possessive pronoun
Hope that helps.
All the best.