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

No

Explanation While the spelling and basic dictionary meaning of "pesquisa" are identical in both dialects, there are notable differences in typical usage and pronunciation:

• Usage: In Brazil, "pesquisa" is the standard, natural term for academic or scientific research (pesquisa científica). In Portugal, while "pesquisa" can be used, the word "investigação" is much more common and natural when referring to scientific or academic endeavors. Furthermore, when referring to opinion polls, Portuguese people frequently use the word "sondagem" instead of "pesquisa."
• Grammar: The way the word is used in continuous actions differs. A Brazilian would use the gerund (fazendo uma pesquisa), whereas a Portuguese person would use the preposition "a" + infinitive (a fazer uma pesquisa).
• Pronunciation: In Brazilian Portuguese, the vowels are generally more open and the rhythm is more melodic. In Continental Portuguese, vowels are much more "reduced" (often sounding almost silent or swallowed), and the "s" at the end of words or before certain consonants often takes a "sh" ([ʃ]) sound.

Brazilian Portuguese Examples

1. Estou fazendo uma pesquisa sobre o clima. (I am doing research about the climate.)
2. A pesquisa de mercado revelou dados importantes. (The market research revealed important data.)
3. Fiz uma pesquisa rápida no Google. (I did a quick search on Google.)
4. A pesquisa de opinião mostrou que o governo está popular. (The opinion poll showed that the government is popular.)
5. Ele dedica a vida à pesquisa científica. (He dedicates his life to scientific research.)

Continental Portuguese Examples

1. Estou a fazer uma pesquisa sobre o clima. (I am doing research about the climate.)
2. A pesquisa de mercado revelou dados importantes. (The market research revealed important data.)
3. Fiz uma pesquisa rápida no Google. (I did a quick search on Google.)
4. A sondagem de opinião mostrou que o governo está popular. (The opinion poll showed that the government is popular.)
5. Ele dedica a vida à investigação científica. (He dedicates his life to scientific research.)