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

Yes

The word "amar" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels tend to be more open and the pronunciation is more melodic and "vocalized." In Continental Portuguese, unstressed vowels are often more closed or even reduced to the point of being nearly silent, and the rhythm is more stress-timed.

Brazilian Portuguese Examples

1. Eu amo minha família. (I love my family.)
2. Ela ama viajar pelo Brasil. (She loves traveling through Brazil.)
3. Nós amamos comer pizza no domingo. (We love eating pizza on Sunday.)
4. Você sabe o quanto eu te amo? (Do you know how much I love you?)
5. Eu amo esse filme! (I love this movie!)

Continental Portuguese Examples

1. Eu amo a minha família. (I love my family. Note: EP frequently uses the definite article "a" before possessives.)
2. Ela ama viajar por Portugal. (She loves traveling through Portugal.)
3. Nós amamos comer pizza ao domingo. (We love eating pizza on Sundays. Note: EP uses "ao domingo" to express habitual actions.)
4. Sabes o quanto eu te amo? (Do you know how much I love you? Note: EP uses the "tu" conjugation "sabes" more naturally than the "você" conjugation used in Brazil.)
5. Eu amo este filme! (I love this movie! Note: EP adheres more strictly to the use of "este" for objects close to the speaker.)