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

Yes

The word "moeda" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are more open and clearly articulated. In Continental Portuguese, unstressed vowels are frequently reduced or nearly silent, making the word sound much more like "mo'da."

Brazilian Portuguese examples:

1. Eu não tenho nenhuma moeda no bolso. (I don't have any coins in my pocket.)
2. A moeda brasileira é o Real. (The Brazilian currency is the Real.)
3. Você tem uma moeda de um real? (Do you have a one-real coin?)
4. O valor da moeda caiu hoje. (The value of the currency fell today.)
5. Preciso de moedas para o parquímetro. (I need coins for the parking meter.)

Continental Portuguese examples:

1. Não tenho moedas no bolso. (I don't have coins in my pocket.)
2. A moeda oficial de Portugal é o Euro. (The official currency of Portugal is the Euro.)
3. Tens uma moeda de um cêntimo? (Do you have a one-cent coin?)
4. O valor da moeda está instável. (The value of the currency is unstable.)
5. Deixa as moedas no balcão. (Leave the coins on the counter.)

(Note: In the third Portuguese example, "cêntimo" is used instead of "centavo" to reflect natural usage in Portugal when referring to small denominations.)