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

No.

While the literal meanings of colar (to glue/paste) and the noun colated (necklace) are identical in both dialects, there are significant differences in slang and typical usage:

• Slang (Brazil): In Brazil, "colar" is widely used informally to mean "to show up," "to arrive," or "to join a group" (e.g., "Cola aí!"). In Portugal, this usage is not standard; a Portuguese person would more likely use aparecer (to appear/show up) or juntar-se (to join).
• Slang (Brazil): In Brazil, "colar" is common slang for cheating on an exam (colar na prova). In Portugal, the preferred term is copiar.
• Vocabulary Context: While the verb remains the same for "gluing," the object being glued often changes. A Brazilian uses adesivo for a sticker, whereas a Portuguese person uses autocolante.

Brazilian Portuguese Examples:

1. "Cola aqui em casa mais tarde!" (Come over to my house later!)
2. "Ele colou todas as respostas na prova." (He cheated on all the answers on the test.)
3. "Eu preciso colar essa foto no caderno." (I need to glue this photo in the notebook.)
4. "A gente vai ao parque, cola com a gente!" (We are going to the park, join us!)
5. "O adesivo não está colando direito." (The sticker is not sticking properly.)

European Portuguese Examples:

1. "Aparece lá em casa mais tarde!" (Show up at my house later!)
2. "Ele copiou todas as respostas no exame." (He cheated on all the answers on the exam.)
3. "Eu preciso colar esta fotografia no caderno." (I need to glue this photograph in the notebook.)
4. "Nós vamos ao parque, junta-te a nós!" (We are going to the park, join us!)
5. "O autocolante não está a colar bem." (The sticker is not sticking well.)