Saying "phụ nữ" is more polite than saying "người đàn bà". In addition, the word "phụ nữ" describes both girls and married woman, while "người đàn bà" only describes married woman.

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"Phụ nữ" is a more general and neutral word, indicating all women who are single or married. "Đàn bà" is more often used to indicate middle-aged or older women, usually married. If it is used to indicate a young woman, then it emphatically implies that she has got married.

"phụ nữ" is a more formal way of saying " người đàn bà"