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

Yes

The word "saúde" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only significant difference is in pronunciation:

• In Brazilian Portuguese, the vowels are generally more open and the syllables are more clearly articulated. Depending on the region, the final "de" is often pronounced with a palatalized "dji" sound.
• In Continental Portuguese, the pronunciation is more "closed" and "clipped." Unstressed vowels are often reduced or almost swallowed, which can make the word sound much shorter or more muffled to a Brazilian ear.

Brazilian Portuguese Examples

1. "Desejo muita saúde para você." (I wish you much health.)
2. "Saúde! Vamos comemorar!" (Cheers! Let's celebrate!)
3. "Você precisa cuidar da sua saúde." (You need to take care of your health.)
4. "Ele está com a saúde muito boa." (He is in very good health.)
5. "(After someone sneezes) Saúde!" (Bless you!)

Continental Portuguese Examples

1. "Desejo-lhe muita saúde." (I wish you much health.)
2. "Saúde! Um brinde à nossa vitória!" (Cheers! A toast to our victory!)
3. "É fundamental zelar pela saúde." (It is fundamental to look after one's health.)
4. "Ele encontra-se com a saúde impecável." (He is in impeccable health.)
5. "(After someone sneezes) Saúde!" (Bless you!)