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

Yes

The word "costuma" (the third-person singular present of the verb costumar) is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The primary difference is pronunciation: in many regions of Portugal, the "s" is pronounced as a "sh" sound ([kuʃˈtumɐ]), and the vowels are more closed, whereas in Brazil, the "s" is often a sibilant [s] and the vowels are more open ([kosˈtuma]). Additionally, while the word itself is the same, the lexical context (the words that typically accompany it) varies significantly between the two countries.

Brazilian Portuguese Examples

1. Ele costuma tomar café da manhã cedo. (He usually has breakfast early.)
2. Ela costuma viajar para a praia. (She usually travels to the beach.)
3. O ônibus costuma atrasar muito. (The bus usually runs very late.)
4. Meu cachorro costuma latir para estranhos. (My dog usually barks at strangers.)
5. A gente costuma comer pizza no fim de semana. (We usually eat pizza on the weekend.)

Portuguese (Continental) Examples

1. Ele costuma tomar o pequeno-almoço cedo. (He usually has breakfast early.)
2. Ela costuma viajar para o litoral. (She usually travels to the coast.)
3. O autocarro costuma atrasar muito. (The bus usually runs very late.)
4. O cão costuma ladrar para estranhos. (The dog usually barks at strangers.)
5. Ele costuma comer pizza ao fim de semana. (He usually eats pizza on the weekend.)