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

No

While the spelling and the fundamental meaning of "minha" (my) are identical, there is a difference in usage and syntax. In Continental Portuguese, it is standard and much more common to precede the possessive pronoun with a definite article (e.g., a minha). In Brazilian Portuguese, the use of the article is optional and is frequently omitted, especially in natural, informal speech. Additionally, when expressing the same ideas, a Portuguese person would use different auxiliary structures (the infinitive vs. the gerund) and different regional vocabulary.

Brazilian Portuguese

1. Minha mãe me ligou agora. (My mother called me just now.)
2. Minha amiga é muito legal. (My friend is very cool.)
3. Essa é minha ideia. (This is my idea.)
4. Minha caneta sumiu. (My pen disappeared.)
5. Minha cachorra está dormindo. (My dog is sleeping.)

European Portuguese

1. A minha mãe ligou-me agora. (My mother called me just now.)
2. A minha amiga é muito gira. (My friend is very pretty/cool.)
3. Esta é a minha ideia. (This is my idea.)
4. A minha caneta desapareceu. (My pen disappeared.)
5. A minha cadela está a dormir. (My dog is sleeping.)