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

No.

While the spelling and fundamental meaning of "senhor" are identical, there are significant differences in usage, grammar, and pronunciation.

• Usage: In Brazil, "o senhor" (and "a senhora") is a ubiquitous way to address elders, strangers, or superiors as a respectful substitute for the pronoun você. In Portugal, while "o senhor" is used for respect, the social application is often more strictly tied to formal distance, and people frequently prefer to address others using their title or name rather than using "senhor" as a direct pronoun replacement.
• Grammar: The placement of object pronouns in sentences containing "senhor" differs. Brazilians heavily favor proclisis (placing the pronoun before the verb, e.g., "o senhor me ajuda"), whereas Portuguese speakers prefer enclisis (placing the pronoun after the verb, e.g., "o senhor ajuda-me").
• Pronunciation: Brazilian Portuguese features more open vowels and a more phonetic articulation of the "r." European Portuguese involves significant vowel reduction, where unstressed vowels often become nearly silent, making the word sound much shorter.

Brazilian Portuguese

1. O senhor pode me ajudar? (Can you help me?)
2. O senhor viu meu documento? (Did you see my document?)
3. Bom dia, senhor Marcos. (Good morning, Mr. Marcos.)
4. O senhor quer um café? (Do you want a coffee?)
5. Como o senhor está hoje? (How are you today?)

European Portuguese

1. Pode ajudar-me? (Can you help me?)
2. Viu o meu documento? (Did you see my document?)
3. Bom dia, Sr. Marcos. (Good morning, Mr. Marcos.)
4. Gostaria de um café? (Would you like a coffee?)
5. Está tudo bem consigo? (Is everything well with you?)