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

Yes

The word "associação" is identical in spelling, meaning, and grammar in both Brazilian and Continental Portuguese. The only differences lie in pronunciation.

In Brazilian Portuguese, the vowels are generally more "open" and the rhythm is more melodic (syllable-timed). The nasal diphthong "-ão" is pronounced with a very clear, resonant nasalization. In Continental Portuguese, unstressed vowels tend to be "reduced" or almost swallowed (vowel reduction), leading to a more "closed" and staccato-like rhythm.

Brazilian Portuguese Examples

1. Eu faço parte de uma associação de moradores. (I am part of a residents' association.)
2. A associação entre o açúcar e o câncer é preocupante. (The association between sugar and cancer is worrying.)
3. Ele trabalha na associação comercial da cidade. (He works at the city's commercial association.)
4. Não existe nenhuma associação entre esses dois fatos. (There is no association between these two facts.)
5. A associação de pais e mestres organizou a festa. (The PTA [Parents and Teachers Association] organized the party.)

Continental Portuguese Examples

1. Sou membro de uma associação de moradores. (I am a member of a residents' association.)
2. A associação entre o açúcar e o cancro é preocupante. (The association between sugar and cancer is worrying.)
3. Ele trabalha na associação comercial da cidade. (He works at the city's commercial association.)
4. Não existe nenhuma associação entre estes dois factos. (There is no association between these two facts.)
5. A associação de pais e mestres organizou a festa. (The PTA organized the party.)