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

No

While the spelling and core meaning of "instrutor" are identical, there is a difference in typical usage. In Portugal, "instrutor" is generally reserved for specific, practical, or technical roles (such as driving, military, or sports instruction). For professional, vocational, or corporate training/courses, a Portuguese person is much more likely to use the word formador. Additionally, the vocabulary surrounding the word differs, such as the Brazilian use of "academia" versus the Portuguese "ginásio."

Brazilian Portuguese Examples:

1. O instrutor de direção foi muito paciente comigo. (The driving instructor was very patient with me.)
2. O instrutor da academia me explicou o exercício. (The gym instructor explained the exercise to me.)
3. O instrutor de mergulho verificou o equipamento. (The diving instructor checked the equipment.)
4. Ele trabalha como instrutor de voo. (He works as a flight instructor.)
5. O instrutor de informática deu uma aula prática. (The IT instructor gave a practical lesson.)

Continental Portuguese Examples:

1. O professor de condução foi muito paciente comigo. (The driving instructor was very patient with me.)
2. O treinador do ginásio explicou-me o exercício. (The gym instructor/trainer explained the exercise to me.)
3. O instrutor de mergulho verificou o equipamento. (The diving instructor checked the equipment.)
4. Ele trabalha como instrutor de voo. (He works as a flight instructor.)
5. O formador de informática deu uma aula prática. (The IT trainer gave a practical lesson.)