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

No.

While the spelling and grammar are identical, there is a difference in typical usage and the semantic scope of the word.

In Brazilian Portuguese, "ginástica" is a broad, generic term used to describe various types of physical exercise, such as aerobics, calisthenics, or "localized fitness" (ginástica localizada). It is common to use the word to refer to any light-to-moderate workout routine.

In Continental Portuguese, "ginástica" is much more specifically associated with the sport of gymnastics (such as artistic or rhythmic gymnastics). When a Portuguese person wants to refer to a general workout, a gym session, or aerobic exercise, they are more likely to use terms such as ginásio (gym), treino (training/workout), fitness, or aeróbica.

Brazilian Portuguese Examples

1. Eu faço ginástica todos os dias para manter a forma. (I do gymnastics/exercise every day to stay in shape.)
2. A aula de ginástica localizada é muito cansativa. (The localized fitness class is very tiring.)
3. Ela adora fazer ginástica no parque. (She loves doing gymnastics/exercise in the park.)
4. A ginástica ajuda a melhorar a postura. (Gymnastics/exercise helps improve posture.)
5. Preciso de uma aula de ginástica para queimar calorias. (I need a fitness/gymnastics class to burn calories.)

Continental Portuguese Examples

1. Eu vou ao ginásio todos os dias para manter a forma. (I go to the gym every day to stay in shape.)
2. A aula de aeróbica é muito cansativa. (The aerobics class is very tiring.)
3. Ela adora treinar no parque. (She loves training in the park.)
4. O exercício físico ajuda a melhorar a postura. (Physical exercise helps improve posture.)
5. Preciso de uma aula de fitness para queimar calorias. (I need a fitness class to burn calories.)