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

Yes

The word "piscina" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is pronunciation: Brazilian Portuguese features more open vowels and a clearer articulation of syllables, while Continental Portuguese is characterized by vowel reduction, where unstressed vowels are much more closed or neutralized.

Brazilian Portuguese

1. Eu gosto de nadar na piscina. (I like swimming in the pool.)
2. A piscina está muito limpa. (The pool is very clean.)
3. As crianças estão brincando na piscina. (The children are playing in the pool.)
4. Você viu a piscina nova do vizinho? (Did you see the neighbor's new pool?)
5. Vamos fazer um lanche na beira da piscina. (Let's have a snack by the poolside.)

Continental Portuguese

1. Eu vou nadar à piscina. (I am going to swim in the pool.)
2. A piscina está muito limpa. (The pool is very clean.)
3. As crianças estão a brincar na piscina. (The children are playing in the pool.)
4. Viste a piscina nova do vizinho? (Did you see the neighbor's new pool?)
5. Vamos fazer um lanche à beira da piscina. (Let's have a snack by the poolside.)