Is the word esposa the same in Brazilian and European Portuguese?

No

While the spelling and fundamental meaning of "esposa" are identical in both dialects, there are differences in grammar, typical usage, and pronunciation.

• Grammar/Usage: In Brazilian Portuguese, it is common to omit the definite article before possessive pronouns (e.g., "Minha esposa"). In Continental Portuguese, the use of the definite article is standard and expected (e.g., "A minha esposa").
• Typical Usage: In Brazil, "esposa" is often perceived as a formal or even "stiff" term, whereas "mulher" is the much more natural and common choice for casual, everyday conversation. In Portugal, "esposa" is used more naturally across a wider range of social settings, including informal ones.
• Pronunciation: Brazilian Portuguese features more open vowels, whereas Continental Portuguese features more closed or reduced vowels (often making unstressed vowels nearly silent).

Brazilian Portuguese Examples

1. Minha esposa trabalha no tribunal. (My wife works at the courthouse.)
2. Apresentei minha esposa ao diretor. (I introduced my wife to the director.)
3. Minha esposa é uma excelente advogada. (My wife is an excellent lawyer.)
4. A reunião foi com minha esposa e eu. (The meeting was with my wife and me.)
5. Minha esposa viajou a negócios. (My wife traveled on business.)

Continental Portuguese Examples

1. A minha mulher trabalha no hospital. (My wife works at the hospital.)
2. Apresentei a minha mulher ao diretor. (I introduced my wife to the director.)
3. A minha mulher é uma excelente médica. (My wife is an excellent doctor.)
4. A reunião foi com a minha mulher e eu. (The meeting was with my wife and me.)
5. A minha mulher viajou por trabalho. (My wife traveled for work.)