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

Yes

The word "estudos" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• Brazilian Portuguese: The vowels tend to be more "open" and clearly articulated. The final "s" is typically pronounced as a sibilant [s] (like the "s" in "sun") in most regions, though in Rio de Janeiro, it may sound like [ʃ] (like "sh").
• Continental Portuguese: The vowels are often "closed" or reduced, making the unstressed "e" almost silent. The final "s" is almost always pronounced as a [ʃ] (the "sh" sound).

Brazilian Portuguese Examples

1. Meus estudos estão atrasados. (My studies are behind schedule.)
2. Ele foca muito nos estudos. (He focuses a lot on his studies.)
3. Os estudos científicos confirmam a ideia. (Scientific studies confirm the idea.)
4. Ela retomou os estudos este ano. (She resumed her studies this year.)
5. Terminei meus estudos de medicina. (I finished my medical studies.)

Continental Portuguese Examples

1. Os meus estudos estão atrasados. (My studies are behind schedule.)
2. Ele foca muito nos estudos. (He focuses a lot on his studies.)
3. Os estudos científicos confirmam a ideia. (Scientific studies confirm the idea.)
4. Ela retomou os estudos este ano. (She resumed her studies this year.)
5. Terminei os meus estudos de medicina. (I finished my medical studies.)