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

No

While the word "corre" is the same conjugation of the verb correr (to run) in both dialects, there is a significant difference in typical usage. In Brazil, "corre" is widely used as a noun (slang) to refer to a "hustle," "daily struggle," or "side job" (e.g., o meu corre). In Portugal, this noun usage is not standard; "corre" is almost exclusively used as a verb.

Brazilian Portuguese Examples

1. "O corre hoje está muito difícil." (The hustle is very difficult today.)
2. "Corre para não perder o ônibus!" (Run so you don't miss the bus!)
3. "Ele tem o seu próprio corre para ganhar dinheiro." (He has his own hustle to make money.)
4. "Eu corro todo dia bem cedo." (I run every day very early.)
5. "O corre de todo dia é muito cansativo." (The daily grind is very tiring.)

Portuguese (Portugal) Examples

1. "Ele corre no parque todas as manhãs." (He runs in the park every morning.)
2. "Corre depressa, que o autocarro já vem!" (Run fast, the bus is already coming!)
3. "Tudo corre bem com o meu trabalho." (Everything is going well with my work.)
4. "O tempo corre muito depressa." (Time runs very fast.)
5. "Corre lá para ver se encontras o teu cão." (Run there to see if you find your dog.)