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

No.

While the spelling and the core meaning of the word are the same, there is a significant difference in grammatical usage.

In Brazilian Portuguese, "brincando" is the gerund form of the verb brincar and is the standard way to express a continuous action (the progressive aspect). When a Brazilian wants to say someone is currently in the act of playing, they use "brincando."

In Continental Portuguese, the gerund is rarely used to express ongoing actions. Instead, the standard construction is the preposition "a" + the infinitive of the verb. Therefore, a person from Portugal would typically say "a brincar" rather than "brincando." Using "brincando" in Portugal sounds very Brazilian and is not the natural way to describe a current action.

Brazilian Portuguese examples:

1. As crianças estão brincando no parque. (The children are playing in the park.)
2. Eu estava brincando com meu cachorro. (I was playing with my dog.)
3. Não leve a sério, eu estou só brincando! (Don't take it seriously, I'm just joking!)
4. Eles passaram a tarde brincando de esconde-esconde. (They spent the afternoon playing hide-and-seek.)
5. Você está brincando com fogo. (You are playing with fire.)

Continental Portuguese examples:

1. As crianças estão a brincar no parque. (The children are playing in the park.)
2. Eu estava a brincar com o meu cão. (I was playing with my dog.)
3. Não leves a sério, eu estou só a brincar! (Don't take it seriously, I'm just joking!)
4. Eles passaram a tarde a brincar às escondidas. (They spent the afternoon playing hide-and-seek.)
5. Estás a brincar com fogo. (You are playing with fire.)