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

No

The difference lies in usage and meaning regarding clothing. In Brazil, "terno" is the standard word for a formal business suit (jacket and trousers). In Portugal, the word "terno" is not used to refer to this garment; instead, the word "fato" is used. While "terno" can theoretically refer to a set of three items in both dialects, its primary everyday association in Brazil is the clothing item, whereas a Portuguese person would find the use of "terno" for clothing to be incorrect.

Brazilian Portuguese Examples

1. Ele comprou um terno novo para a entrevista de emprego. (He bought a new suit for the job interview.)
2. Você precisa passar o terno antes de sair. (You need to iron the suit before leaving.)
3. O terno azul marinho é muito elegante para casamentos. (The navy blue suit is very elegant for weddings.)
4. Ele não gosta de usar terno no calor do Rio de Janeiro. (He doesn't like wearing a suit in the heat of Rio de Janeiro.)
5. O terno dele ficou apertado nos ombros. (His suit became tight in the shoulders.)

Continental Portuguese Examples

1. Ele comprou um fato novo para a entrevista de emprego. (He bought a new suit for the job interview.)
2. Tu precisas de passar o fato antes de saíres. (You need to iron the suit before you leave.)
3. O fato azul-marinho é muito elegante para casamentos. (The navy blue suit is very elegant for weddings.)
4. Ele não gosta de usar fato no calor do verão. (He doesn't like wearing a suit in the summer heat.)
5. O fato dele ficou apertado nos ombros. (His suit became tight in the shoulders.)