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

No

While the core meaning and spelling of "terminar" are identical in both dialects, there are significant differences in pronunciation and typical usage:

• Pronunciation: In Brazilian Portuguese, the vowels are generally more open, and the final "r" is often softened, swallowed, or aspirated (sounding like an "h"). In Continental Portuguese, the vowels are more closed or reduced, and the "r" is typically more distinct or tapped.
• Usage (Grammar/Syntax): The most notable difference is in how the verb is used to express continuous actions. Brazilians almost exclusively use the gerund (terminando). Portuguese people typically use the preposition "a" + the infinitive (a terminar). Furthermore, while "terminar" is common in both, Portuguese speakers frequently substitute it with "acabar" when referring to finishing a task or a period of time.

Brazilian Portuguese Examples:

1. Eu estou terminando o meu dever de casa. (I am finishing my homework.)
2. Eles terminaram o namoro mês passado. (They ended their relationship last month.)
3. O jogo está terminando agora. (The game is ending now.)
4. Eu preciso terminar esse projeto logo. (I need to finish this project soon.)
5. Você já terminou de ler o livro? (Have you finished reading the book?)

Continental Portuguese Examples:

1. Estou a terminar o meu trabalho de casa. (I am finishing my homework.)
2. Eles terminaram o namoro no mês passado. (They ended their relationship last month.)
3. O jogo está a terminar agora. (The game is ending now.)
4. Preciso de terminar este projeto brevemente. (I need to finish this project soon.)
5. Já acabaste de ler o livro? (Have you finished reading the book?)