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

Yes

The word "gosta" is identical in meaning, spelling, and grammatical function (third-person singular present indicative of the verb gostar) in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the unstressed "o" is often subject to vowel reduction, sounding more like a short, muffled "a" or "u" ([gɔstɐ] or [gɔstə]). In Continental Portuguese, the "o" is more clearly and distinctly articulated as a mid-open vowel ([gɔstɐ]). Additionally, in certain Brazilian dialects (such as in Rio de Janeiro), the "s" in the syllable coda of "gos-ta" may be pronounced as a "sh" sound ([ˈɡɔʃta]), whereas in Portugal, it remains a "s" sound ([ˈɡɔstɐ]).

Brazilian Portuguese Examples

1. Ele gosta muito de chocolate. (He likes chocolate a lot.)
2. Ele gosta de brincar com o cachorro. (He likes to play with the dog.)
3. Ele gosta de andar de ônibus. (He likes to ride the bus.)
4. Ele gosta de comer um lanche. (He likes to eat a snack.)
5. Ele gosta de viajar de avião. (He likes to travel by plane.)

Portuguese Examples

1. Ele gosta muito de chocolate. (He likes chocolate a lot.)
2. Ele gosta de brincar com o cão. (He likes to play with the dog.)
3. Ele gosta de andar de autocarro. (He likes to ride the bus.)
4. Ele gosta de comer um lanche. (He likes to eat a snack.)
5. Ele gosta de viajar de avião. (He likes to travel by plane.)