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

Yes

The word "sapatos" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation.

In Brazilian Portuguese, the vowels are generally "open" and clearly articulated. The "s" at the end of the word is typically pronounced as a soft /s/ (though in Rio de Janeiro and other coastal regions, it may sound like "sh"). In Continental Portuguese, the vowels are much more "closed" or reduced, often making the unstressed syllables sound almost swallowed. Furthermore, the terminal "s" in Portugal is almost always pronounced as a "sh" sound (/ʃ/).

Brazilian Portuguese Examples

1. Eu preciso comprar sapatos novos. (I need to buy new shoes.)
2. Seus sapatos estão muito sujos. (Your shoes are very dirty.)
3. Onde você comprou esses sapatos? (Where did you buy these shoes?)
4. Eu não gosto de usar sapatos apertados. (I don't like wearing tight shoes.)
5. Vou guardar meus sapatos no armário. (I am going to put my shoes in the closet.)

Portuguese (Portugal) Examples

1. Preciso comprar uns sapatos novos. (I need to buy some new shoes.)
2. Os teus sapatos estão muito sujos. (Your shoes are very dirty.)
3. Onde é que compraste esses sapatos? (Where did you buy those shoes?)
4. Não gosto de usar sapatos que apertem. (I don't like wearing shoes that are tight.)
5. Vou pôr os meus sapatos no armário. (I am going to put my shoes in the cupboard.)