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

Yes

The word "mandam" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are typically more open and clearly articulated. In Continental Portuguese, unstressed vowels are often reduced or "swallowed," making the word sound more clipped and the second syllable much shorter.

Brazilian Portuguese Examples

1. Eles mandam mensagens pelo celular. (They send messages via cell phone.)
2. Eles mandam o ônibus para a escola. (They send the bus to the school.)
3. Eles mandam muita propaganda na internet. (They send/post a lot of advertising on the internet.)
4. Eles mandam o lanche por delivery. (They send the snack via delivery.)
5. Eles mandam o pessoal de trem para a capital. (They send the staff by train to the capital.)

Continental Portuguese Examples

1. Eles mandam mensagens pelo telemóvel. (They send messages via mobile phone.)
2. Eles mandam o autocarro para a escola. (They send the bus to the school.)
3. Eles mandam muita publicidade na internet. (They send/post a lot of advertising on the internet.)
4. Eles mandam o lanche por entrega. (They send the snack via delivery.)
5. Eles mandam o pessoal de comboio para a capital. (They send the staff by train to the capital.)