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

No

While the core meaning and spelling of "pensar" are identical in both dialects, there are significant differences in grammar and typical usage regarding how the word is integrated into sentences.

1. Grammatical Construction (Continuous Aspect): In Brazil, when expressing an ongoing action, the gerund is used (estou pensando). In Portugal, the standard construction is the preposition a followed by the infinitive (estou a pensar).
2. Preposition Usage: In Brazil, the verb precisar (frequently paired with pensar) often omits the preposition "de" (e.g., preciso pensar). In Portugal, the use of "de" is grammatically standard and expected (preciso de pensar).
3. Pronoun/Conjugation Context: The way "pensar" is conjugated in conversation changes because Brazilians typically use você (third-person conjugation), while Portuguese people frequently use tu (second-person conjugation).

Brazilian Portuguese Examples

1. Eu estou pensando em viajar nas férias. (I am thinking about traveling on my vacation.)
2. No que você está pensando agora? (What are you thinking about right now?)
3. Eu não pensei nisso antes. (I didn't think about that before.)
4. Você precisa pensar no seu futuro. (You need to think about your future.)
5. Eu penso que ele vai chegar atrasado. (I think that he is going to arrive late.)

Continental Portuguese Examples

1. Estou a pensar em viajar nas férias. (I am thinking about traveling on my vacation.)
2. Em que estás a pensar agora? (What are you thinking about right now?)
3. Não pensei nisso antes. (I didn't think about that before.)
4. Precisas de pensar no teu futuro. (You need to think about your future.)
5. Penso que ele vai chegar atrasado. (I think that he is going to arrive late.)