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

No

While the spelling and core meaning (to be in a temporary state or location) are identical, there is a fundamental difference in its grammatical usage and pronunciation.

• Grammar/Usage: In Brazilian Portuguese, "estar" is typically used with the gerund to express ongoing actions (e.g., estou falando). In Continental Portuguese, "estar" is used with the preposition a followed by the infinitive (e.g., estou a falar).
• Pronunciation: Brazilian Portuguese tends to have more open, clearly articulated vowels. In contrast, Continental Portuguese features significant vowel reduction, where unstressed vowels are often shortened or nearly swallowed, making the rhythm of the language sound more "consonantal."

Brazilian Portuguese Examples:

1. Eu estou comendo uma maçã. (I am eating an apple.)
2. Você está muito cansado. (You are very tired.)
3. Nós estamos morando no Brasil. (We are living in Brazil.)
4. Onde está o meu celular? (Where is my cell phone?)
5. Eles estão brincando no parque. (They are playing in the park.)

Continental Portuguese Examples:

1. Eu estou a comer uma maçã. (I am eating an apple.)
2. Tu estás muito cansado. (You are very tired.)
3. Nós estamos a morar no Brasil. (We are living in Brazil.)
4. Onde está o meu telemóvel? (Where is my mobile phone?)
5. Eles estão a brincar no parque. (They are playing in the park.)