die Frau
woman
An adult female person.
Die Frau am Nachbartisch liest ein Buch.
The woman at the next table is reading a book.

woman / wife
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woman
An adult female person.
Die Frau am Nachbartisch liest ein Buch.
The woman at the next table is reading a book.

Whether 'Frau' means any woman or a wife depends on the context. A possessive pronoun like 'meine' (my), 'seine' (his), or 'ihre' (her/their) almost always points to the meaning 'Ehefrau' (wife).
Eine Frau hat nach Ihnen gefragt.
A woman asked for you.
As a polite form of address, 'Frau' always stands without an article directly before the last name. This form is used both when addressing someone directly and when speaking about a person.
Guten Tag, Frau Weber, schön Sie zu sehen.
Good afternoon, Ms. Weber, nice to see you.
In German, 'Frau' is the neutral and usual form of address for any adult woman, regardless of her marital status. German does not distinguish between married and unmarried women in this form of address.
Sehr geehrte Frau Dr. Bauer, anbei sende ich Ihnen die Unterlagen.
Dear Dr. Bauer, please find attached the documents.
man
'der Mann' and 'die Frau' form a clear contrast when talking about adult people: a man is male, a woman is female. Both words can also be used to mean a spouse or partner. In that case, 'mein Mann' means husband and 'meine Frau' means wife. So context is important: if you are talking generally about people, it is about gender and age. If you are speaking with a possessive word like 'mein' or 'seine', it may be about a marriage or steady partnership.

Meine Frau hat gestern den Termin beim Arzt vereinbart.
My wife made the doctor's appointment yesterday.
Der Mann an der Rezeption hilft den Gästen mit dem Formular.
The man at the reception desk helps the guests with the form.