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

Yes

The spelling, meaning, and grammatical function of "sem" are identical in both Brazilian and Continental Portuguese. The only difference is in pronunciation:

• Brazilian Portuguese: The nasal vowel often undergoes diphthongization, meaning it sounds slightly like there is a very faint "i" or "y" sound at the end (approximating [sẽj]).
• Continental Portuguese: The pronunciation is more closed and purely nasalized, without the diphthongization typical of most Brazilian regions (approximating [sẽ]).

Brazilian Portuguese Examples

1. Eu não consigo viver sem café. (I cannot live without coffee.)
2. Ele saiu de casa sem as chaves. (He left the house without his keys.)
3. Estamos sem sinal de celular aqui. (We are without cell signal here.)
4. A criança ficou sem o brinquedo. (The child was left without the toy.)
5. Não faz sentido fazer isso sem planejamento. (It makes no sense to do this without planning.)

Continental Portuguese Examples

1. Eu não consigo viver sem café. (I cannot live without coffee.)
2. Ele saiu de casa sem as chaves. (He left the house without his keys.)
3. Estamos sem sinal de telemóvel aqui. (We are without mobile signal here.)
4. A criança ficou sem o brinquedo. (The child was left without the toy.)
5. Não faz sentido fazer isto sem planeamento. (It makes no sense to do this without planning.)