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

No

While the spelling and fundamental meaning (a female coach or trainer) are the same, there is a difference in typical usage regarding professional or educational contexts.

In Brazil, "treinadora" is frequently used for anyone providing instruction, whether in sports, fitness, or even corporate workshops. In Portugal, while "treinadora" is the standard word for sports (soccer, athletics, etc.) and animal training, the word formadora is much more common when referring to someone who provides professional, vocational, or educational training (e.g., someone teaching a computer course or a corporate workshop).

Brazilian Portuguese Examples

1. A treinadora de futebol é muito exigente. (The soccer coach is very demanding.)
2. Contratei uma treinadora para me ajudar na academia. (I hired a trainer to help me at the gym.)
3. A treinadora de cães ensinou o comando "fica". (The dog trainer taught the "stay" command.)
4. Nossa treinadora está muito orgulhosa da equipe. (Our coach is very proud of the team.)
5. A treinadora de tênis chegou atrasada para o treino. (The tennis coach arrived late for the practice.)

Continental Portuguese Examples

1. A treinadora de ténis é excelente. (The tennis coach is excellent.)
2. A formadora do curso de informática explicou a matéria. (The IT course instructor explained the subject.)
3. A treinadora de cães tem muita experiência com raças grandes. (The dog trainer has a lot of experience with large breeds.)
4. A formadora da empresa ministrou um workshop de gestão. (The company instructor conducted a management workshop.)
5. A nossa treinadora de atletismo é muito rigorosa. (Our athletics coach is very rigorous.)