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

No

While "primo" retains its primary meaning of "cousin" (a family member) in both Brazil and Portugal, there is a significant difference in typical usage. In Brazilian Portuguese, "primo" is frequently used as a colloquial slang term to address a friend, similar to "bro," "buddy," or "dude." In Continental Portuguese, this usage is not standard; using "primo" to refer to a non-relative would likely cause confusion. Additionally, there is a difference in grammar/syntax: Portuguese speakers in Portugal almost always use a definite article before the possessive pronoun (e.g., "o meu primo"), whereas Brazilians often omit it (meu primo).

Brazilian Portuguese Examples

1. Meu primo mora no Rio de Janeiro. (My cousin lives in Rio de Janeiro.)
2. E aí, primo! Tudo beleza? (Hey, bro! Everything good?) Note: Here, "primo" is used as slang for a friend.
3. Vou sair com uns primos mais tarde. (I'm going out with some buddies later.) Note: Here, "primos" refers to friends, not relatives.
4. Ele é meu primo de consideração. (He is like a cousin to me.)
5. Fala, primo, como você está? (Hey, man, how are you?)

Continental Portuguese Examples

1. O meu primo mora no Rio de Janeiro. (My cousin lives in Rio de Janeiro.)
2. Olá, pá! Tudo bem? (Hello, man! Everything well?) Note: "Pá" is the natural equivalent to the Brazilian slang use of "primo."
3. Vou sair com os meus amigos mais tarde. (I'm going out with my friends later.) Note: "Amigos" is used instead of "primos" to avoid implying a family relationship.
4. Ele é como um irmão para mim. (He is like a brother to me.) Note: A Portuguese person would more naturally use "brother" to express this level of closeness.
5. Então, gajo, como estás? (Hey, dude, how are you?) Note: "Gajo" is a common way to address a male peer informally.