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

No.

While the spelling and fundamental meaning of "relacionar" are identical in both dialects, there are differences in pronunciation and typical usage. In Brazilian Portuguese, vowels are generally more open and clearly articulated. In Continental Portuguese, unstressed vowels undergo significant reduction or "swallowing," making the word sound more clipped. Additionally, there is a difference in syntax/usage regarding the reflexive form: Brazilians frequently use proclisis (placing the pronoun before the verb, e.g., se relacionar), whereas the natural and standard usage in Portugal is enclisis (placing the pronoun after the verb, e.g., relacionar-se).

Brazilian Portuguese

1. Eu não consigo relacionar esses dois fatos. (I can't relate these two facts.)
2. Ela se relaciona muito bem com as pessoas. (She interacts/relates very well with people.)
3. O relatório vai relacionar todos os problemas encontrados. (The report will list all the problems found.)
4. Precisamos relacionar o custo ao benefício. (We need to relate the cost to the benefit.)
5. Ele gosta de se relacionar com pessoas novas. (He likes to interact with new people.)

Continental Portuguese

1. Não consigo relacionar estes dois factos. (I can't relate these two facts.)
2. Ela relaciona-se muito bem com as pessoas. (She interacts/relates very well with people.)
3. O relatório vai relacionar todos os problemas encontrados. (The report will list all the problems found.)
4. Precisamos de relacionar o custo ao benefício. (We need to relate the cost to the benefit.)
5. Ele gosta de relacionar-se com pessoas novas. (He likes to interact with new people.)