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

Yes

The word "conto" is identical in spelling, grammar, and primary meaning in both Brazilian and Continental Portuguese. It serves as a noun meaning "short story" (the literary genre) and as the first-person singular present indicative of the verb contar ("I count" or "I tell"). The only difference is pronunciation. In Brazilian Portuguese, the final "o" is typically pronounced as a clear [u] sound. In Continental Portuguese, there is much more significant vowel reduction, meaning the unstressed final "o" is often much more closed, extremely short, or nearly inaudible.

Brazilian Portuguese Examples

1. Eu conto uma história para a criança antes de dormir. (I tell a story to the child before sleeping.)
2. Eu conto com você para me ajudar no projeto. (I am counting on you to help me with the project.)
3. O escritor publicou um conto maravilhoso este mês. (The writer published a wonderful short story this month.)
4. Eu conto os minutos para as férias chegarem. (I count the minutes for vacation to arrive.)
5. Eu conto as moedas para ver quanto dinheiro eu tenho. (I count the coins to see how much money I have.)

Continental Portuguese Examples

1. Eu conto um conto ao meu filho antes de dormir. (I tell a short story to my son before sleeping.)
2. Eu conto contigo para me ajudares no projeto. (I am counting on you to help me with the project.)
3. O escritor publicou um conto maravilhoso este mês. (The writer published a wonderful short story this month.)
4. Eu conto os minutos para as férias chegarem. (I count the minutes for vacation to arrive.)
5. Eu conto as moedas para ver quanto dinheiro tenho. (I count the coins to see how much money I have.)