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

No.

While the fundamental meaning of the word "treina" (the third-person singular of the verb treinar) is consistent across both dialects, there are significant differences in pronunciation, typical usage, and grammar:

• Pronunciation: In Continental Portuguese, vowels are often "reduced" or swallowed, making the "e" sound almost disappear or sound like a very short "schwa." In Brazilian Portuguese, the vowels are much more open, clear, and fully articulated.
• Typical Usage: In Brazil, "treinar" is used broadly to mean practicing any repetitive task, including music, dance, or studying. In Portugal, "treinar" is much more strictly associated with sports or animal training; for arts and performances, a Portuguese person would almost always use the word ensaiar (to rehearse).
• Grammar: In Brazil, "treina" is frequently used informally as the imperative (command) for the pronoun você. In Portugal, "treina" is the standard, grammatically correct imperative for the pronoun tu.

Brazilian Portuguese Examples

1. Ele treina muito na academia. (He trains a lot at the gym.)
2. Você treina para o concurso? (Are you training/studying for the competition?)
3. Ela treina a coreografia nova. (She practices the new choreography.)
4. Treina o seu cachorro! (Train your dog!)
5. O time treina no campo. (The team trains on the field.)

Continental Portuguese Examples

1. Ele treina muito no ginásio. (He trains a lot at the gym.)
2. Estás a treinar para o concurso? (Are you training/studying for the competition?)
3. Ela ensaia a coreografia nova. (She rehearses the new choreography.)
4. Treina o teu cão! (Train your dog!)
5. A equipa treina no campo. (The team trains on the field.)