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

Yes

The word "carpinteiro" has the exact same meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. It refers to a person skilled in working with wood. The only difference between the two dialects is the pronunciation. In Brazil, the vowels are typically more open and the rhythm is more melodic (syllable-timed), whereas in Portugal, the pronunciation is more stress-timed, often resulting in the reduction or "swallowing" of unstressed vowels.

Brazilian Portuguese Examples

1. Eu preciso contratar um carpinteiro para consertar o portão. (I need to hire a carpenter to fix the gate.)
2. O carpinteiro está fazendo um armário novo para a cozinha. (The carpenter is making a new cabinet for the kitchen.)
3. Meu avô era um carpinteiro muito talentoso. (My grandfather was a very talented carpenter.)
4. O carpinteiro já terminou de lixar a mesa de madeira. (The carpenter has already finished sanding the wooden table.)
5. Você conhece algum carpinteiro que trabalhe aqui no bairro? (Do you know any carpenter who works here in the neighborhood?)

Continental Portuguese Examples

1. Preciso de um carpinteiro para reparar o portão. (I need a carpenter to repair the gate.)
2. O carpinteiro está a fazer um armário novo para a cozinha. (The carpenter is making a new cabinet for the kitchen.)
3. O meu avô era um carpinteiro muito talentoso. (My grandfather was a very talented carpenter.)
4. O carpinteiro já terminou de lixar a mesa de madeira. (The carpenter has already finished sanding the wooden table.)
5. Conheces algum carpinteiro que trabalhe por aqui? (Do you know any carpenter who works around here?)