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

Yes

The word "escritor" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the initial "e" is typically pronounced clearly as an open or mid-vowel [e], and the "r" at the end is often a soft flap. In Continental Portuguese, the initial "e" is frequently reduced to a near-silent, neutral vowel [ɨ], and the "r" may be pronounced with a more retracted or uvular sound depending on the specific region of Portugal.

Brazilian Portuguese Examples

1. Ele quer ser um escritor famoso. (He wants to be a famous writer.)
2. Eu li um livro de um escritor brasileiro incrível. (I read a book by an amazing Brazilian writer.)
3. Ela está escrevendo um novo romance. (She is writing a new novel.)
4. O escritor está assinando autógrafos na livraria. (The writer is signing autographs at the bookstore.)
5. Você conhece algum escritor de ficção científica? (Do you know any science fiction writer?)

Continental Portuguese Examples

1. Ele quer ser um escritor famoso. (He wants to be a famous writer.)
2. Li um livro de um escritor português excelente. (I read a book by an excellent Portuguese writer.)
3. Ela está a escrever um novo romance. (She is writing a new novel.)
4. O escritor está a assinar autógrafos na livraria. (The writer is signing autographs at the bookstore.)
5. Conheces algum escritor de ficção científica? (Do you know any science fiction writer?)