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

Yes

The word "carro" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only differences are phonetic:

• Pronunciation: In Brazil, the "r" is often retroflex (similar to the American English "r") or aspirated depending on the region, and the final "o" is typically pronounced as a clear [u]. In Portugal, the "r" is more alveolar or tapped, and the final unaccented "o" is much more closed, sounding closer to a short [ɐ].

Brazilian Portuguese Examples

1. Eu vou lavar o meu carro hoje. (I am going to wash my car today.)
2. O carro dele é muito rápido. (His car is very fast.)
3. A gente precisa de um carro maior para a viagem. (We need a larger car for the trip.)
4. O carro quebrou no meio da avenida. (The car broke down in the middle of the avenue.)
5. Você viu onde eu estacionei o carro? (Did you see where I parked the car?)

Continental Portuguese Examples

1. Vou lavar o meu carro hoje. (I am going to wash my car today.)
2. O carro dele é muito veloz. (His car is very fast.)
3. Precisamos de um carro maior para a viagem. (We need a larger car for the trip.)
4. O carro avariou no meio da estrada. (The car broke down in the middle of the road.)
5. Viste onde estacionei o carro? (Did you see where I parked the car?)