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

Yes

The word "moro" is identical in both Brazilian and Continental Portuguese. It is the first-person singular present indicative of the verb morar (to reside/to live). There are no differences in meaning, grammar, or spelling.

The only difference lies in pronunciation. In Brazilian Portuguese, the unstressed final "o" is typically reduced to an [u] sound (sounding like "moru"). In Continental Portuguese, while the final "o" can also be reduced, the vowel is often more closed, and the overall rhythm and prosody of the word differ due to the distinct cadence of European Portuguese.

Brazilian Portuguese Examples

1. Eu moro no Rio de Janeiro. (I live in Rio de Janeiro.)
2. Eu moro com meus pais. (I live with my parents.)
3. Eu moro em um apartamento pequeno. (I live in a small apartment.)
4. Eu moro perto do metrô. (I live near the subway.)
5. Eu moro aqui faz dois anos. (I have lived here for two years.)

Continental Portuguese Examples

1. Eu moro no Porto. (I live in Porto.)
2. Eu moro com os meus pais. (I live with my parents.)
3. Eu moro num apartamento pequeno. (I live in a small apartment.)
4. Eu moro perto do metro. (I live near the metro.)
5. Eu moro aqui há dois anos. (I have lived here for two years.)