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

Yes

The word "corro" is identical in both Brazilian and Continental Portuguese regarding its spelling, grammar, and core meaning. It is the first-person singular present indicative of the verb correr (to run). The only difference between the two dialects is the pronunciation: Brazilian Portuguese tends to have more open vowels and a more melodic, syllable-timed rhythm, while Continental Portuguese features more closed or reduced vowels and a stress-timed rhythm.

Brazilian Portuguese Examples

1. Eu corro todo dia no parque. (I run every day in the park.)
2. Corro para não perder o ônibus. (I run so I don't miss the bus.)
3. Sempre corro de manhã cedo. (I always run early in the morning.)
4. Corro muito quando estou atrasado. (I run a lot when I am late.)
5. Eu corro maratonas de vez em quando. (I run marathons once in a while.)

European Portuguese Examples

1. Eu corro todos os dias no parque. (I run every day in the park.)
2. Corro para não perder o autocarro. (I run so I don't miss the bus.)
3. Corro sempre de manhã cedo. (I always run early in the morning.)
4. Corro imenso quando estou atrasado. (I run a lot when I am late.)
5. Corro maratonas ocasionalmente. (I run marathons occasionally.)