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

Yes.

The word "samba" is identical in spelling, meaning, and grammatical function in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the "am" creates a strong nasalized vowel, and the final "a" is typically pronounced as an open [a]. In Continental Portuguese, the final "a" is much more closed or reduced [ɐ], and the "m" is often pronounced more distinctly as a consonant rather than just a nasal marker for the vowel.

Brazilian Portuguese Examples:

1. A gente vai pro samba hoje à noite. (We are going to the samba session tonight.)
2. Esse samba tá muito massa! (This samba is really cool!)
3. Eu amo um samba de raiz. (I love traditional/roots samba.)
4. Vem sambar com a gente! (Come samba with us!)
5. O samba é a cara do Brasil. (Samba is the face/essence of Brazil.)

Continental Portuguese Examples:

1. Nós vamos ao samba hoje à noite. (We are going to the samba session tonight.)
2. Este samba está muito fixe! (This samba is very cool!)
3. Eu adoro samba de raiz. (I adore traditional/roots samba.)
4. Vem dançar samba connosco! (Come dance samba with us!)
5. O samba é a essência do Brasil. (Samba is the essence of Brazil.)