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

Yes

The differences between "nadam" in Brazilian and Continental Portuguese are strictly phonetic. There are no differences in meaning, spelling, or grammatical function. In Brazilian Portuguese, the vowels are typically more open and the nasalization of the final "-am" is more clearly articulated. In Continental Portuguese, unstressed vowels are often reduced or "swallowed," meaning the "a" in "nadam" may be much shorter or nearly silent, resulting in a more compressed sound.

Brazilian Portuguese Examples:

1. Eles nadam no rio de Janeiro. (They swim in Rio de Janeiro.)
2. Vocês nadam muito bem na piscina. (You all swim very well in the pool.)
3. Os meninos nadam no mar todo verão. (The boys swim in the sea every summer.)
4. Eles nadam de manhã cedo. (They swim early in the morning.)
5. As crianças nadam na lagoa. (The children swim in the lagoon.)

Continental Portuguese Examples:

1. Eles nadam no mar todos os dias. (They swim in the sea every day.)
2. Os miúdos nadam na praia. (The kids swim at the beach.)
3. Eles nadam no rio durante o verão. (They swim in the river during the summer.)
4. Os jovens nadam no clube. (The youths swim at the club.)
5. Eles nadam com muita destreza. (They swim with great skill.)