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

Yes.

The word "etiqueta" shares the exact same meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. It refers to both a physical label (such as a price tag or a clothing label) and the concept of social etiquette (manners and rules of behavior). The only significant difference is in pronunciation. In Brazilian Portuguese, the unstressed vowels are more open and clearly articulated, whereas in Continental Portuguese, unstressed vowels are often reduced, shortened, or nearly silent, leading to a more "closed" sound.

Brazilian Portuguese Examples

1. A etiqueta da minha camisa está me incomodando. (The tag on my shirt is bothering me.)
2. Ele não entende nada de etiqueta à mesa. (He understands nothing about table etiquette.)
3. Dá uma olhada na etiqueta para ver o preço. (Take a look at the tag to see the price.)
4. Eu preciso tirar a etiqueta desse casaco. (I need to remove the tag from this jacket.)
5. A etiqueta social exige que você seja educado. (Social etiquette requires you to be polite.)

Continental Portuguese Examples

1. A etiqueta da minha camisola está a incomodar-me. (The tag on my sweater is bothering me.)
2. Ele não percebe nada de etiqueta à mesa. (He doesn't understand anything about table etiquette.)
3. Vê a etiqueta para veres o preço. (Look at the tag to see the price.)
4. Tenho de tirar a etiqueta deste casaco. (I have to remove the tag from this jacket.)
5. A etiqueta social exige que sejas educado. (Social etiquette requires you to be polite.)