Difference between mio and mia?

3

You're quite correct, mio and mia are both the same thing: possessive pronouns
"Mio" is the masculine singular for the 1st person singular, while "mia" is the feminine singular for the 1st person singular.
Just remembering: it must be preceeded by an article, except when in front of names that represent kinship, in the singular.

So, you would say: "Mia madre (no article) scrive con la mia penna (article)" (My mother writes with my pen)

1

Here's a more complete explanation:

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Possessive Pronouns / Adjectives
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The rows represent the "owner".

The columns represent the "owned thing".

Mio / Mia / Miei /Mie

Tuo / Tua / Tuoi / Tue

Suo / Sua / Suoi / Sue

Nostro / Nostra / Nostri / Nostre

Vostro / Vostra / Vostri / Vostre

Loro

They are almost always preceded by articles.

i.e.

"That's ours" [ speaking about a "house" ]

The owner is "Noi" and the owned thing is "House", a feminine, singular thing.
So the correct personal pronoun is in the 4th row & 2nd column: "Nostra"

"Quella è la nostra"

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As for the article:

- Kinship?

[ NO ]
Article on the left of the possessive adjective

[ YES - Singular ]
NO article

[ YES - Plural ]
Article on the left of the possessive adjective

[ YES - Augmented word ]
Article on the left of the possessive adjective

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If you use "Papà" [ Dad - mostly used by children or if you're talking directly to your father ] instead of "Padre" and "Mamma" [ Mom - mostly used by children or if you're talking directly to your mother ] instead of "Madre", you can use the article.

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If the object of your sentence is "casa", you can write it in two ways:

"È la mia casa"
"È casa mia"
[ It's my house ]