Test: does the word sit before a noun, or replace one? Its always sits before a noun, so it is a possessive determiner: The dog wagged its tail. The matching standalone pronoun slot stays empty.
Relevant types at a glance
Possessive determiner. Sits directly before a noun to show ownership. The cat licked its paw.
Possessive pronoun. Replaces a noun entirely, so nothing follows it. That book is yours. In the parallel slot you would say hers, never her.
Personal pronoun. Refers to a person or thing as subject or object. They called her yesterday.
Reflexive pronoun. Points back to the sentence's own subject. He taught himself to cook.
Demonstrative pronoun. Stands alone to point something out. Those are expensive. Compare the determiner use, those shoes.
The tricky spot: 'its' on both lists
One spot in the tables needs a closer look. Its appears under both the determiner and pronoun rows because the paradigm is regular: every person and number gets a determiner form and a pronoun form, so the table fills in its on both sides even though the position test does the sorting in practice. Put it before a noun and it classifies as a possessive determiner, as in The kitten licked its ear.
The pronoun side is where things get awkward. Real possessive pronouns like hers stand alone in place of a noun, as in That seat is hers. English has no established standalone its form used this way, so a pronoun reading never arises in ordinary sentences: its always appears directly before a noun.
So when classifying, trust the position test. Its before a noun is a possessive determiner. Standard grammar paradigms do list its in the pronoun column, right next to forms like hers and theirs, but English speakers never actually use it that way in ordinary speech or writing. That standalone pronoun slot stays empty in practice, so treating its before a noun as a possessive determiner is the practical answer.