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

Yes

The word "usar" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The only differences are:

• Pronunciation: Brazilian Portuguese typically features more open vowels and a more "musical," syllable-timed rhythm. Continental Portuguese features more closed vowels and a stress-timed rhythm, which often makes the unstressed syllables sound almost swallowed or reduced.
• Contextual usage: While "usar" is perfectly correct in both dialects, a Portuguese person may more frequently use the verbs "vestir" (to put on/wear) or "levar" (to wear/carry) when referring to clothing or accessories, whereas Brazilians use "usar" more broadly to cover both the act of dressing and the habit of wearing something.

Brazilian Portuguese Examples:

1. Eu vou usar esse tênis amanhã. (I am going to use/wear those sneakers tomorrow.)
2. Você precisa usar o cinto de segurança. (You need to use the seatbelt.)
3. Ele usa óculos de grau. (He wears prescription glasses.)
4. Nós podemos usar o seu celular? (Can we use your cell phone?)
5. Ela usa maquiagem para trabalhar. (She wears makeup for work.)

European Portuguese Examples:

1. Eu vou usar estas sapatilhas amanhã. (I am going to use/wear these sneakers tomorrow.)
2. Precisas de usar o cinto de segurança. (You need to use the seatbelt.)
3. Ele usa óculos de leitura. (He wears reading glasses.)
4. Podemos usar o seu telemóvel? (Can we use your cell phone?)
5. Ela usa maquilhagem para trabalhar. (She wears makeup for work.)