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

Yes

The word "história" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels tend to be more open and the rhythm is more syllable-timed (each syllable receives a similar duration). In Continental Portuguese, vowels in unstressed positions are often more closed or even reduced (almost disappearing), and the rhythm is more stress-timed, giving the language a different cadence.

Brazilian Portuguese Examples

1. Eu adoro ler histórias de terror. (I love reading horror stories.)
2. A história do Brasil é muito interessante. (The history of Brazil is very interesting.)
3. Não me venha com essa história! (Don't come to me with that story! / Don't give me that excuse!)
4. Ele contou uma história muito legal. (He told a very cool story.)
5. Preciso estudar para a prova de história. (I need to study for the history test.)

Continental Portuguese Examples

1. Adoro ler histórias de terror. (I love reading horror stories.)
2. A história de Portugal é muito interessante. (The history of Portugal is very interesting.)
3. Não me venhas com essa história! (Don't come to me with that story!)
4. Ele contou uma história muito gira. (He told a very nice story.)
5. Preciso estudar para o exame de história. (I need to study for the history exam.)