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

Yes

The word "ganha" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The difference is purely phonetic. In Brazilian Portuguese, the pronunciation is more "open," and the final "a" is clearly and distinctly articulated. In Continental Portuguese, unstressed vowels (like the final "a") are often reduced or "swallowed," making the word sound much shorter and the final vowel nearly neutralized.

Brazilian Portuguese Examples

1. Ele ganha muito dinheiro. (He earns a lot of money.)
2. O time ganha o jogo. (The team wins the game.)
3. Ela ganha um presente de aniversário. (She gets a birthday present.)
4. Você ganha muito tempo com esse atalho. (You gain a lot of time with this shortcut.)
5. Quem ganha o prêmio? (Who wins the prize?)

Portuguese (Continental) Examples

1. Ele ganha muito dinheiro. (He earns a lot of money.)
2. O clube vence o jogo. (The club wins the game.)
3. Ela ganha um prémio. (She wins a prize.)
4. Tu ganhas muito espaço com este móvel. (You gain a lot of space with this piece of furniture.)
5. Quem vence a competição? (Who wins the competition?)