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

Yes

The spelling, grammar, and meaning of the word "noz" are identical in both Brazilian and Continental Portuguese. In both dialects, "noz" refers specifically to a walnut, while "nozes" is used to refer to walnuts in the plural or to the category of "nuts" in general. The only difference is in pronunciation:

• In Brazilian Portuguese, the final "z" is voiced, sounding like the English "z" in "zebra" (/noz/).
• In Continental Portuguese, the final "z" is typically unvoiced and palatalized, sounding like the "sh" in "shoe" (/noʃ/).

Brazilian Portuguese Examples

1. Eu adoro comer noz com mel. (I love eating walnut with honey.)
2. Tem um pedacinho de noz no meu bolo. (There is a little piece of walnut in my cake.)
3. A casca da noz é bem dura. (The walnut shell is quite hard.)
4. Eu prefiro nozes do que amendoim. (I prefer nuts to peanuts.)
5. Vou comprar nozes no mercado hoje. (I am going to buy nuts at the market today.)

Continental Portuguese Examples

1. Gostava de comer uma noz, por favor. (I would like to eat a walnut, please.)
2. Este doce tem muita noz. (This sweet has a lot of walnut.)
3. A noz é muito boa para a saúde. (The walnut is very good for one's health.)
4. Comprei nozes para o lanche. (I bought nuts for the snack.)
5. É muito difícil abrir esta noz. (It is very difficult to open this walnut.)