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

No.

While the spelling and the 3rd-person meaning (his/her/their) are identical, there is a significant difference in typical usage regarding the 2nd person (addressing someone directly).

In Brazil, "seu" is the standard possessive pronoun used when addressing someone as você (the common, neutral/informal way to say "you"). Therefore, "seu" is the most frequent way to say "your" in daily Brazilian conversation.

In Portugal, "seu" is strictly associated with the 3rd person. When addressing someone informally as tu (the standard way to say "you" to friends, family, or peers), a Portuguese person uses teu. While a Portuguese person can use "seu" to mean "your," they only do so in very formal or distant contexts when addressing someone as o senhor or a senhora.

Brazilian Portuguese examples:

1. Onde está o seu celular? (Where is your cell phone?)
2. Eu gosto muito do seu carro. (I like your car very much.)
3. Você esqueceu o seu casaco aqui. (You forgot your jacket here.)
4. Como está o seu trabalho? (How is your job?)
5. O seu cachorro é muito fofo. (Your dog is very cute.)

European Portuguese examples:

1. Onde está o teu telemóvel? (Where is your mobile phone?)
2. Eu gosto muito do teu carro. (I like your car very much.)
3. Tu esqueceste o teu casaco aqui. (You forgot your jacket here.)
4. Como está o teu trabalho? (How is your job?)
5. O teu cão é muito fofo. (Your dog is very cute.)