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

Yes

The word "vidro" is identical in meaning, spelling, and grammatical gender (masculine) in both Brazilian and Continental Portuguese. The only differences lie in the pronunciation (specifically the phonetic realization of vowels and the rhythmic stress) and the syntactic patterns of the sentences in which it is used (such as the choice of accompanying verbs or the placement of pronouns).

Brazilian Portuguese Examples

1. Eu quebrei o vidro da janela. (I broke the window glass.)
2. O copo é feito de vidro. (The cup is made of glass.)
3. Cuidado para não sujar o vidro. (Be careful not to get the glass dirty.)
4. O vidro do carro está trincado. (The car window is cracked.)
5. Ela comprou um vaso de vidro. (She bought a glass vase.)

Continental Portuguese Examples

1. Parti o vidro da janela. (I broke the window glass. — Note: "Partir" is more common than "quebrar" in Portugal, and the subject "Eu" is often omitted.)
2. O copo é de vidro. (The cup is made of glass.)
3. Tem cuidado, que o vidro está sujo. (Be careful, because the glass is dirty. — Note: Use of "tem cuidado" and the conjunction "que" is a very natural construction.)
4. O vidro do automóvel está partido. (The car window is broken. — Note: "Automóvel" is frequently used instead of "carro", and "partido" is the standard term for broken.)
5. Comprou um vaso de vidro. (She bought a glass vase. — Note: The subject is typically omitted in natural speech.)