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

No

While the core meaning of the word "bola" (a spherical object) remains the same, there are significant differences in typical usage, vocabulary choice for related objects, and grammatical construction.

In Brazil, the word is used in the specific term "bola de gude" to refer to marbles, whereas in Portugal, the word "bola" is replaced by the diminutive "bolinhas." Additionally, while a Brazilian would use the gerund ("brincando") to describe an ongoing action, a Portuguese person would typically use the preposition "a" followed by the infinitive ("a brincar"). There are also slight differences in natural verbs used alongside the word, such as the preference for "jogar" (to throw/play) in Brazil versus "atirar" or "lançar" in Portugal.

Brazilian Portuguese Examples

1. Eu chutei a bola com muita força. (I kicked the ball very hard.)
2. A criança está brincando com a bola de gude. (The child is playing with the marble.)
3. Ele perdeu a bola durante o jogo. (He lost the ball during the game.)
4. A bola de futebol é nova. (The soccer ball is new.)
5. Jogue a bola para mim, por favor. (Throw the ball to me, please.)

Portuguese (Portugal) Examples

1. Eu chutei a bola com muita força. (I kicked the ball very hard.)
2. A criança está a brincar com as bolinhas. (The child is playing with the marbles.)
3. Ele perdeu a bola durante o jogo. (He lost the ball during the game.)
4. A bola de futebol é nova. (The soccer ball is new.)
5. Atira a bola para mim, por favor. (Throw the ball to me, please.)