"vuoi" is "you want", singular. While "vuole" could be used either for the 3rd person singular feminine, for example: "Lei vuole una mela" = She wants an apple; or for the formal way of "you" when you talk to a stranger older than you (or equal in age if are both adults, meanwhile is not used among young people), and in formal situations (for example at the post office). So for example at the market: "A: Vuole anche una mela? B: Sì, grazie" "A: Would you also like an apple? B: Yes, thank you."

I think you wanted to say 'vuole'..which is for the 3rd person, singular. but to say 'you want' you just have to say 'tu vuoi'

1st meaning Informal: "cosa vuoi" -> what do you want? courtesy form: "cosa vuole?" -> what do you want? 2nd meaning "cosa vuole (lui)?" -> what does he want?

anyway, the formal ''Vuole" is disappearing. So don't give too much importance to this thing. Just concentrate on simple and direct things :)

Vuoi and vuole can be used into a formal or informal sentences. At a shop: "Anli, vuoi compare questo vestito?", a person who knows you well ask you: "Anli, do you want to buy this dress?". "Signora (madama), vuole acquistare questo vestito", a shop assistant ask you: " Madame, would you love to buy this dress?" infinitive: volere (to want) 2nd person: "tu vuoi", informal and common - Lei vuole, very formal (it's disappearing) 3rd person: "lui (he) vuole" "ella (she) vuole", both are informal and common