Re: simple qustion
I was always taught that my, your, his, its in 'Have you seen ... new coat?' were possessive adjectives - they functioned in a similar way to adjectives. Mine, yours, his, its in, "Here is Mary's coat; where is ...?' were possessive pronouns - they stood in place of a noun.
I then discovered some American school grammars in which both forms were called possessive pronouns. In 'his coat', his stands for the noun John's (for example); in 'Whose coat is this? It is his', his stands for John's (coat).
The current situation in Britain appears to be that the first group are now called (possesive) determiners, the second group possessive pronouns.
As both billmcd and emsr2d2 noted, the possessive pronoun its rarely used. The possessive determiner/adjective its is quite common. Note that neither form has an apostrophe. It's is used only as a contracted form of it is or it has.
Context is always important; labelling is rarely important.