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

No.

The word "pasta" has differences in its scope of meaning and typical usage between the two variants. In Brazil, "pasta" can refer to a "paste" (such as toothpaste or peanut butter) as well as the food item (Italian pasta), although the word "massa" is also frequently used for food. In Portugal, "pasta" is almost exclusively used to refer to a "paste" or a "folder"; when referring to the food item (spaghetti, etc.), Portuguese people almost always use the word massa. Additionally, there are grammatical differences in common phrases, such as the Brazilian use of the singular "pasta de dente" versus the more common Portuguese plural "pasta de dentes."

Brazilian Portuguese Examples

1. "Eu gosto de comer pasta de amendoim no café da manhã." (I like to eat peanut butter for breakfast.)
2. "A pasta de dente acabou." (The toothpaste ran out.)
3. "Crie uma pasta nova no seu computador." (Create a new folder on your computer.)
4. "Organize os arquivos nesta pasta." (Organize the files in this folder.)
5. "Eu adoro comer pasta italiana." (I love eating Italian pasta.)

Continental Portuguese Examples

1. "Eu gosto de comer pasta de amendoim ao pequeno-almoço." (I like to eat peanut butter for breakfast.)
2. "A pasta de dentes acabou." (The toothpaste ran out.)
3. "Cria uma pasta nova no teu computador." (Create a new folder on your computer.)
4. "Organiza os ficheiros nesta pasta." (Organize the files in this folder.)
5. "Eu adoro comer massa italiana." (I love eating Italian pasta.)