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

Yes

The word "projeto" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. Following the 1990 Orthographic Agreement, the spelling was standardized across all Portuguese-speaking countries, removing the "c" that previously appeared in the European "projecto."

The primary difference lies in pronunciation and phonology:

• Brazil: The pronunciation tends to be "syllable-timed." Vowels are more open and clearly articulated. The "e" in "projeto" is often pronounced as a bright, open [ɛ].
• Portugal: The pronunciation is more "stress-timed." Vowels are often reduced or "swallowed" (vowel reduction), making the word sound more clipped. The "e" may be pronounced as a more closed [e].

While the word itself remains the same, the surrounding sentence structure (the "natural expression") often differs, particularly regarding the use of the gerund versus the infinitive.

Brazilian Portuguese Examples

1. Eu estou fazendo um projeto novo para a faculdade. (I am making a new project for college.)
2. Esse projeto é muito legal! (This project is very cool!)
3. A gente precisa de um projeto de reciclagem. (We need a recycling project.)
4. O projeto da empresa vai dar muito trabalho. (The company's project is going to be a lot of work.)
5. O projeto de lei foi aprovado ontem. (The bill was approved yesterday.)

European Portuguese Examples

1. Estou a fazer um projeto novo para a faculdade. (I am making a new project for college.)
2. Este projeto é muito giro! (This project is very nice/cool!)
3. Nós precisamos de um projeto de reciclagem. (We need a recycling project.)
4. O projeto da empresa vai dar muito trabalho. (The company's project is going to be a lot of work.)
5. O projeto de lei foi aprovado ontem. (The bill was approved yesterday.)