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

No.

While the fundamental meaning of "prisão" (prison or imprisonment) is identical in both dialects, there are differences in typical usage, grammatical agreement, and pronunciation.

In Brazil, "prisão" is frequently used to refer to the act of an arrest (e.g., "a prisão do suspeito"). In Portugal, while "prisão" can be used, it is much more natural to use the word "detenção" to describe the act of being taken into custody, reserving "prisão" more specifically for the institution or the state of being imprisoned. Furthermore, the term for house arrest differs grammatically: Brazilians use the masculine/neutral "prisão domiciliar," whereas the Portuguese use the feminine "prisão domiciliária." Finally, pronunciation differs significantly; Brazilian Portuguese features more open vowels and a different realization of the nasal diphthong "ão" compared to the more closed and tense vowels of Continental Portuguese.

Brazilian Portuguese Examples

1. A prisão do suspeito aconteceu ontem à noite. (The arrest of the suspect happened last night.)
2. Ele foi condenado à prisão perpétua. (He was sentenced to life imprisonment.)
3. Ele está cumprindo pena em uma prisão de segurança máxima. (He is serving his sentence in a maximum-security prison.)
4. O juiz determinou a prisão domiciliar do réu. (The judge ordered house arrest for the defendant.)
5. A fuga da prisão causou grande alvoroço na cidade. (The prison escape caused great uproar in the city.)

Portuguese (Portugal) Examples

1. A detenção do suspeito aconteceu ontem à noite. (The arrest of the suspect happened last enough night.)
2. Ele foi condenado à prisão perpétua. (He was sentenced to life imprisonment.)
3. Ele está a cumprir pena numa prisão de segurança máxima. (He is serving his sentence in a maximum-security prison.)
4. O juiz determinou a prisão domiciliária do réu. (The judge ordered house arrest for the defendant.)
5. A fuga da prisão causou grande alvoroço na cidade. (The prison escape caused great uproar in the city.)