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

Yes

The meaning, spelling, and grammatical usage of "grave" are identical in both Brazilian and Continental Portuguese. In both dialects, the word is used as an adjective to describe something serious or severe (e.g., a disease or an error) and to describe a low pitch or frequency (e.g., a voice or a sound). The only difference is pronunciation:

• Brazilian Portuguese: The final "e" is typically reduced and pronounced as a short, light [i] sound (sounding like "gra-vee").
• Continental Portuguese: The final "e" is a more closed, neutralized vowel [ɨ], which is a sound that does not exist in English, often sounding more "muffled" or swallowed than the Brazilian version.

Brazilian Portuguese Examples:

1. O paciente está em estado grave. (The patient is in serious condition.)
2. Ele tem uma voz muito grave. (He has a very deep voice.)
3. Isso é um erro muito grave. (That is a very serious mistake.)
4. A situação no hospital está grave. (The situation at the hospital is serious.)
5. Eles enfrentam problemas graves. (They are facing serious problems.)

Continental Portuguese Examples:

1. O doente está num estado grave. (The patient is in a serious condition.)
2. Ele tem uma voz bastante grave. (He has a quite deep voice.)
3. Isto é um erro muito grave. (This is a very serious mistake.)
4. A situação no hospital está grave. (The situation at the hospital is serious.)
5. Eles enfrentam problemas graves. (They are facing serious problems.)