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

Yes

The word "greve" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are typically more open and the pronunciation is more melodic and elongated. In Continental Portuguese, the unstressed vowels are more closed or "swallowed," making the word sound more clipped and brief.

Brazilian Portuguese Examples:

1. A greve de ônibus vai atrasar todo mundo. (The bus strike is going to delay everyone.)
2. Os professores entraram em greve hoje. (The teachers went on strike today.)
3. Não tem aula por causa da greve. (There is no class because of the strike.)
4. A greve de fome chamou a atenção do mundo. (The hunger strike drew the world's attention.)
5. O metrô está parado devido à greve. (The subway is stopped due to the strike.)

Continental Portuguese Examples:

1. A greve de autocarros vai causar confusão. (The bus strike will cause confusion.)
2. Os professores decidiram fazer greve. (The teachers decided to go on strike.)
3. Não há aulas devido à greve. (There are no classes due to the strike.)
4. A greve de fome despertou o interesse internacional. (The hunger strike aroused international interest.)
5. O metro está parado por causa da greve. (The metro is stopped because of the strike.)