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

No

While the spelling, meaning, and conjugation of "está" are identical in both dialects, there is a fundamental difference in its typical usage regarding the continuous aspect (actions happening right now). In Brazilian Portuguese, "está" is used with the gerund (e.g., está fazendo), whereas in Continental Portuguese, "está" is used with the preposition "a" followed by the infinitive (e.g., está a fazer). Additionally, there is a major difference in pronunciation: Brazilian Portuguese is more syllable-timed with clearly articulated, open vowels, while Continental Portuguese is more stress-timed and tends to "swallow" or reduce unstressed vowels.

Brazilian Portuguese Examples

1. O cachorro está correndo no parque. (The dog is running in the park.)
2. Onde está o seu celular? (Where is your cell phone?)
3. A comida está muito gostosa. (The food is very tasty.)
4. Ela está estudando para a prova. (She is studying for the exam.)
5. O tempo está ficando frio. (The weather is getting cold.)

Portuguese (Portugal) Examples

1. O cão está a correr no parque. (The dog is running in the park.)
2. Onde está o teu telemóvel? (Where is your mobile phone?)
3. A comida está muito saborosa. (The food is very tasty.)
4. Ela está a estudar para o exame. (She is studying for the exam.)
5. O tempo está a ficar frio. (The weather is getting cold.)