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

Yes

The word "desconto" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• Brazilian Portuguese: The vowels are generally more "open" and clearly articulated. The unstressed final "o" is pronounced as a clear [u] sound, and the rhythm of the word is more melodic and even.
• Continental Portuguese: There is a heavy use of vowel reduction. Unstressed vowels are often shortened or almost "swallowed" (elided). A Portuguese person might pronounce the word more like d'scon-tu, where the initial "e" is nearly silent.

Brazilian Portuguese Examples

1. "Você tem algum desconto para pagamento à vista?" (Do you have any discount for cash payment?)
2. "Eu consegui um desconto enorme nessa loja de roupas." (I got a huge discount in that clothing store.)
3. "O desconto não apareceu no meu carrinho de compras." (The discount did not appear in my shopping cart.)
4. "Aproveite o desconto de 50% em toda a loja hoje!" (Take advantage of the 50% discount storewide today!)
5. "Houve um desconto indevido no meu salário este mês." (There was an undue deduction in my salary this month.)

Continental Portuguese Examples

1. "Pode fazer-me um desconto se eu comprar dois artigos?" (Can you give me a discount if I buy two items?)

2. "Este artigo tem um desconto de dez por cento." (This item has a ten percent discount.)

3. "Pedi um desconto, mas o vendedor não aceitou." (I asked for a discount, but the salesman did not accept.)

4. "O desconto é aplicado diretamente no total da fatura." (The discount is applied directly to the total of the invoice.)

5. "Tive um desconto no imposto de renda este ano." (I had a deduction in my income tax this year.)