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

No

The difference lies in typical usage. While the grammatical definition of "na" (the contraction of the preposition em + the feminine article a) is the same, Brazilians frequently use "na" colloquially to indicate movement or destination (e.g., "I am going to the pharmacy"). In Portugal, "na" is used strictly to indicate a static location or position (being inside something). To express movement toward a destination, a Portuguese person would typically use "à" (the contraction of the preposition a + the feminine article a).

Brazilian Portuguese usage:

1. Vou na farmácia agora. (I am going to the pharmacy now.)
2. Ela passou na escola hoje. (She stopped by the school today.)  3. O livro está na mochila. (The book is in the backpack.)
3. Estamos na sala de aula. (We are in the classroom.)
4. Passa na minha casa mais tarde. (Stop by my house later.)

Continental Portuguese usage:

1. Vou à farmácia agora. (I am going to the pharmacy now.)
2. Ela passou à escola hoje. (She stopped by the school today.)
3. O livro está na mochila. (The book is in the backpack.)
4. Estamos na sala de aula. (We are in the classroom.)
5. Passa à minha casa mais tarde. (Stop by my house later.)