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

No

While the spelling and fundamental meaning of "quarta" are identical in both dialects, there is a difference in typical usage and pronunciation:

• Usage: In Brazil, it is extremely common to use "quarta" as a standalone noun to refer to Wednesday (short for quenta-feira). In Portugal, while "quarta" is used as an ordinal number, it is much less common to use it alone to refer to the day; Portuguese speakers typically prefer the full term "quarta-feira."
• Pronunciation: There is a significant difference in how the vowels are pronounced. Brazilian Portuguese tends to use more open vowels (e.g., the "a" sounds like [a]), whereas Continental Portuguese frequently employs vowel reduction, where unstressed vowels are "closed" or reduced (e.g., the "a" sounds more like a neutral [ɐ]).

Brazilian Portuguese Examples

1. Eu tenho médico na quarta. (I have a doctor's appointment on Wednesday.)
2. A quarta série era a minha favorita. (Fourth grade was my favorite.)
3. A gente se vê na quarta? (Shall we see each other on Wednesday?)
4. Ela ficou em quarta posição na corrida. (She finished in fourth position in the race.)
5. Esta é a quarta vez que eu venho aqui. (This is the fourth time I have come here.)

Continental Portuguese Examples

1. Eu tenho médico na quarta-feira. (I have a doctor's appointment on Wednesday.)
2. O quarto ano era o meu favorito. (The fourth year was my favorite.)
3. Encontramo-nos na quarta-feira? (Shall we meet on Wednesday?)
4. Ela ficou em quarta posição na corrida. (She finished in fourth position in the race.)
5. Esta é a quarta vez que eu venho aqui. (This is the fourth time I have come here.)