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

No

While the fundamental meanings of "tocar" (to play an instrument, to ring, or to touch) are the same, there are differences in typical usage, grammar, and the vocabulary it interacts with.

• Usage/Vocabulary: In Brazil, "tocar" is used informally to mean "to drive" (e.g., tocar o carro), a usage that is not common in Portugal, where conduzir is the standard. Furthermore, the objects associated with the verb change (e.g., Brazilians say violão for acoustic guitar, while Portuguese say guitarra; Brazilians say celular, while Portuguese say telemóvel).
• Usage/Context: In Brazil, the expression for knocking on a door is typically bater na porta, whereas in Portugal, tocar à porta (to ring/knock) is a very common way to express the same idea.
• Grammar: The imperative (command) form differs significantly due to the use of você in Brazil versus the use of tu in much of Portugal.

Brazilian Portuguese Examples

1. Eu adoro tocar violão. (I love playing the acoustic guitar.)
2. O celular tocou muito alto durante a reunião. (The cell phone rang very loud during the meeting.)
3. Por favor, não toque na comida. (Please, do not touch the food.)
4. Ele gosta de tocar o carro em estradas de terra. (He likes to drive the car on dirt roads. — Informal usage)
5. Ela toca a música com muita emoção. (She plays the song with much emotion.)

Continental Portuguese Examples

1. Eu adoro tocar guitarra. (I love playing the acoustic guitar.)
2. O telemóvel tocou muito alto durante a reunião. (The mobile phone rang very loud during the meeting.)
3. Por favor, não toques na comida. (Please, do not touch the food. — Using the 'tu' form)
4. Ele toca à porta para avisar que chegou. (He knocks/rings the bell to announce he has arrived.)
5. Ele gosta de conduzir o carro em estradas de terra. (He likes to drive the car on dirt roads.)