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

No.

While the spelling, meaning, and grammatical gender of "sábado" are identical in both varieties, there is a difference in typical usage regarding the preposition used to denote time, as well as differences in pronunciation. In Brazil, it is standard to use the preposition "no" (a contraction of em + o) to refer to Saturdays. In Portugal, it is much more common to use "ao" (a contraction of a + o) to denote recurring events or habits. Additionally, the pronunciation of the vowels differs, with Brazilian Portuguese often featuring different vowel openness depending on the region.

Brazilian Portuguese Examples

1. Eu vou à praia no sábado. (I am going to the beach on Saturday.)
2. No sábado, a gente vai ao cinema. (On Saturday, we are going to the movies.)
3. Você tem planos para o sábado? (Do you have plans for Saturday?)
4. Eu sempre estudo no sábado de manhã. (I always study on Saturday morning.)
5. O shopping fecha mais tarde no sábado. (The mall closes later on Saturday.)

Portuguese Examples

1. Eu vou ao cinema ao sábado. (I go to the cinema on Saturdays.)
2. Costumo visitar os meus avós ao sábado. (I usually visit my grandparents on Saturdays.)
3. Ao sábado, o mercado está muito cheio. (On Saturdays, the market is very crowded.)
4. Ele joga futebol ao sábado. (He plays football on Saturdays.)
5. Ao sábado, as lojas abrem mais tarde. (On Saturdays, the shops open later.)