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

Yes

The meaning, spelling, and grammar of the word "novela" are identical in both Brazilian and Continental Portuguese. It refers to a serialized television drama (soap opera) or a short work of fiction (novella). The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open, and the rhythm is syllable-timed, making the "o" sound more like an "o" in "open." In Continental Portuguese, the rhythm is stress-timed, and unstressed vowels are often reduced or "swallowed"; specifically, the "o" in "novela" is much more closed, sounding nearly like a "u" ([nuˈvelɐ]).

Brazilian Portuguese Examples

1. Eu adoro assistir à novela das nove. (I love watching the 9 PM soap opera.)
2. A novela de hoje foi muito emocionante. (Today's soap opera was very emotional.)
3. Você viu o que aconteceu na novela ontem? (Did you see what happened in the soap opera yesterday?)
4. Essa novela é um grande sucesso no Brasil. (This soap opera is a huge success in Brazil.)
5. Eu gosto de ler uma novela curta antes de dormir. (I like to read a short novella before sleeping.)

Continental Portuguese Examples

1. Gostaste da novela de ontem? (Did you like yesterday's soap opera?)
2. Eu estou a ver a telenovela agora. (I am watching the telenovela now.)
3. A novela está a ser muito boa nesta temporada. (The soap opera is being very good this season.)
4. Aquela telenovela é muito dramática. (That telenovela is very dramatic.)
5. Vi a novela na televisão. (I saw the soap opera on television.)