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

Yes

The meaning, spelling, and grammar of "apoio" are identical in both Brazilian and European Portuguese. The differences are limited to pronunciation and the syntax of the sentences in which it is used. In Brazilian Portuguese, the vowels are generally more open and the rhythm is more syllable-timed. In European Portuguese, unstressed vowels (such as the final "o" in "apoio") are often reduced or more closed, and the rhythm is more stress-timed. Additionally, while "apoio" remains the same word, a Portuguese person will use different pronoun placements and possessive adjectives (e.g., using teu instead of seu) when expressing the same idea.

Brazilian Portuguese Examples:

1. Eu te apoio nessa decisão. (I support you in this decision.)
2. Ele precisa de muito apoio emocional. (He needs a lot of emotional support.)
3. O governo vai dar apoio aos pequenos negócios. (The government is going to provide support to small businesses.)
4. O seu apoio é essencial para o projeto. (Your support is essential for the project.)
5. Use este objeto como apoio para a câmera. (Use this object as a support for the camera.)

European Portuguese Examples:

1. Eu apoio-te nessa decisão. (I support you in this decision.)
2. Ele precisa de muito apoio emocional. (He needs a lot of emotional support.)
3. O governo vai dar apoio aos pequenos negócios. (The government is going to provide support to small businesses.)
4. O teu apoio é essencial para o projeto. (Your support is essential for the project.)
5. Usa este objeto como apoio para a câmara. (Use this object as a support for the camera.)