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

Yes

The meaning, spelling, and grammar of the word "barba" are identical in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are generally more open and the rhythm is more "syllable-timed," meaning each syllable is given relatively equal weight. In Continental Portuguese, there is significant vowel reduction, where unstressed vowels are often shortened or almost silenced, and the rhythm is more "stress-timed."

Brazilian Portuguese examples:

1. Eu preciso fazer a minha barba. (I need to trim my beard.)
2. Ele está com a barba muito grande. (His beard is very big/long.)
3. Ele decidiu deixar a barba crescer. (He decided to let his beard grow.)
4. A barba dele é bem macia. (His beard is very soft.)
5. Ele usa óleo para cuidar da barba. (He uses oil to take care of his beard.)

Continental Portuguese examples:

1. Eu preciso de aparar a barba. (I need to trim the beard.)
2. Ele está com a barba muito comprida. (His beard is very long.)
3. Ele decidiu deixar a barba crescer. (He decided to let the beard grow.)
4. A barba dele é muito macia. (His beard is very soft.)
5. Ele usa óleo para cuidar da barba. (He uses oil to take care of the beard.)