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

Yes

The word botas (the noun meaning "boots") is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• Vowels: In Brazil, the "o" is typically an open vowel [ɔ] (similar to the "o" in the English word "hot"). In Portugal, the "o" is a closed, more muffled vowel [o].
• The "s" sound: In many regions of Brazil (such as São Paulo), the final "s" is pronounced as a soft [s]. However, in Rio de Janeiro and other coastal regions, it is pronounced as [ʃ] (like the "sh" in "shoe"). In Portugal, the "s" is almost always pronounced as [ʃ].

Brazilian Portuguese Examples

1. Eu comprei um par de botas novas. (I bought a pair of new boots.)
2. Essas botas de couro são muito resistentes. (These leather boots are very durable.)
3. Você viu onde eu guardei minhas botas? (Did you see where I put my boots?)
4. Ele gosta de usar botas de cano curto. (He likes to wear ankle boots.)
5. As botas ficaram sujas de lama durante a trilha. (The boots got dirty with mud during the trail.)

Continental Portuguese Examples

1. Eu comprei um par de botas novas. (I bought a pair of new boots.)
2. Estas botas de couro são muito resistentes. (These leather boots are very durable. — Note: "Estas" is used instead of "essas" to refer to something close to the speaker.)
3. Viste onde eu guardei as minhas botas? (Did you see where I put my boots? — Note: "Viste" is used instead of "Você viu" to reflect natural 2nd person usage.)
4. Ele gosta de usar botas de cano curto. (He likes to wear ankle boots.)
5. As botas ficaram sujas de lama durante a caminhada. (The boots got dirty with mud during the hike. — Note: "Caminhada" is used instead of "trilha" as the standard term for a trek/hike.)