You and I are family words: anh, chị, em, cô, chú, ba / mẹ and con, thầy / cô and em
address by age and relationship
Pattern: [kinship word] = you / I · em ↔ anh / chị · con ↔ cô / chú · con ↔ ba / má or ba / mẹ (S), bố / mẹ (N) · em ↔ thầy / cô · bác sĩ = you
In Saigon: ba / má; ba / mẹ · In Hà Nội: bố / mẹ
Typed without accents: anh, chi, em, co, chu, ba, ma, bo, me, con, thay
In everyday Vietnamese, "I" and "you" aren't fixed words. You call each person by a family word that fits their age and your relationship, and the same word works both ways: it means "you" when you talk to them, and "I" when they talk to you.
Age decides first. A man a little older than you is anh, a woman chị, and you are em, whether you're a man or a woman. Someone younger is em, and you are anh or chị. Someone your parents' age is cô (a woman) or chú (a man), and you are con: Dạ, con chào cô. In Hà Nội you'd be cháu. Someone older than your parents is bác, and someone your grandparents' age is ông (a man) or bà (a woman).
In the family the words are literal. Children call their parents ba and mẹ (many Saigon families say má; in Hà Nội bố and mẹ), and parents call a child con. A teacher is thầy (a man) or cô (a woman), and students are usually em. You can address a doctor as bác sĩ.
Couples say anh and em, the man usually anh. With an adult whose age you can't guess, anh or chị is the safe, friendly choice, and a name can follow: chị Lan. The neutral tôi and bạn sound distant between people who know each other.
Examples
Highlighted words are what Saigon and Hà Nội say differently.
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Chị ơi, cho em hỏi chút.
Excuse me, can I ask you something? (to a woman a bit older)
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Saigon
Dạ, con chào cô.
Hà Nội
Dạ, cháu chào cô.
Hello. (to a woman your mother's age)
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Mẹ ơi, con đói quá.
Mum, I'm so hungry.
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Anh nhớ em.
I miss you. (a man to his partner)