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

No.

While the fundamental meanings of "conta" (bank account, calculation, or restaurant bill) remain the same, there is a difference in typical usage and grammar regarding utility bills. In Brazil, "conta" is the standard word for electricity, water, or phone bills (e.g., conta de luz). In Portugal, while "conta" is used for restaurant bills, the word "fatura" is much more common and natural when referring to utility bills. Additionally, there is a subtle difference in the use of articles and prepositions: Brazilians often use "conta de [service]," while Portuguese people more frequently use "conta da/do [service]."

Brazilian Portuguese Examples

1. A conta de luz chegou hoje. (The electricity bill arrived today.)
2. Você pode me trazer a conta, por favor? (Can you bring me the bill, please?)
3. Preciso pagar a conta de água. (I need to pay the water bill.)
4. Ele abriu uma conta no banco ontem. (He opened a bank account yesterday.)
5. Vou fazer as contas para ver se sobra dinheiro. (I am going to do the math to see if there is money left.)

Continental Portuguese Examples

1. A fatura da luz chegou hoje. (The electricity bill arrived today.)
2. Pode trazer-me a conta, por favor? (Can you bring me the bill, please?)
3. Preciso de pagar a fatura da água. (I need to pay the water bill.)
4. Ele abriu uma conta no banco ontem. (He opened a bank account yesterday.)
5. Vou fazer as contas para ver se sobra dinheiro. (I am going to do the math to see if there is money left.)