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

Yes

The word "vermelha" is identical in spelling, meaning, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels tend to be more open and the rhythm of speech is more syllabic. In Continental Portuguese, the pronunciation is more "closed," with unstressed vowels often being reduced or even elided, and the rhythm of the language is more stress-timed (placing more emphasis on the stressed syllables).

Brazilian Portuguese

1. Ela está usando uma blusa vermelha. (She is wearing a red blouse.)
2. A maçã está bem vermelha. (The apple is very red.)
3. Eu vi uma flor vermelha no jardim. (I saw a red flower in the garden.)
4. A tinta da caneta vermelha acabou. (The red pen's ink ran out.)
5. A luz vermelha do semáforo acendeu. (The red light of the traffic light turned on.)

Continental Portuguese

1. Ela está a usar uma blusa vermelha. (She is wearing a red blouse.)
2. A maçã está muito vermelha. (The apple is very red.)
3. Eu vi uma flor vermelha no jardim. (I saw a red flower in the garden.)
4. A caneta vermelha ficou sem tinta. (The red pen ran out of ink.)
5. A luz vermelha do semáforo acendeu. (The red light of the traffic light turned on.)