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

No

While the core dictionary meanings of dirigir (to direct, to manage, or to address) are identical in both varieties, there is a significant difference in typical usage regarding vehicles. In Brazil, dirigir is the standard, everyday verb used for operating a car. In Portugal, while dirigir is understood, the verb conduzir is the much more natural and common choice for driving a vehicle. In Portugal, dirigir is more heavily associated with the act of directing a group, a company, or a film.

Brazilian Portuguese Examples

1. Eu adoro dirigir de madrugada. (I love driving in the early morning hours.)
2. Ele ainda está aprendendo a dirigir. (He is still learning how to drive.)
3. Você sabe dirigir carro manual? (Do you know how to drive a manual car?)
4. É perigoso dirigir com o celular na mão. (It is dangerous to drive with a cell phone in your hand.)
5. Ela tirou a habilitação mês passado. (She got her driver's license last month.)

European Portuguese Examples

1. Eu adoro conduzir de madrugada. (I love driving in the early morning hours.)
2. Ele ainda está a aprender a conduzir. (He is still learning how to drive.)
3. Sabes conduzir carro manual? (Do you know how to drive a manual car?)
4. É perigoso conduzir com o telemóvel na mão. (It is dangerous to drive with a mobile phone in your hand.)
5. Ela tirou a carta de condução o mês passado. (She got her driver's license last month.)