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

Yes

The word "caderno" has the exact same meaning (notebook) and spelling in both Brazilian and Continental Portuguese. The only differences lie in pronunciation. In Brazil, the vowels tend to be more open and the rhythm is more syllable-timed, whereas in Portugal, vowels are often more closed or reduced, and the rhythm is more stress-timed. Additionally, while the word is the same, the way it is used in a sentence (syntax) often differs due to the use of pronouns and verb forms.

Brazilian Portuguese Examples

1. Eu esqueci meu caderno na escola. (I forgot my notebook at school.)
2. Você pode me emprestar um caderno? (Can you lend me a notebook?)
3. Eu estou escrevendo no meu caderno. (I am writing in my notebook.)
4. Preciso comprar um caderno novo para o curso. (I need to buy a new notebook for the course.)
5. O caderno está cheio de anotações. (The notebook is full of notes.)

Continental Portuguese Examples

1. Esqueci o meu caderno na escola. (I forgot my notebook at school.)
2. Podes emprestar-me um caderno? (Can you lend me a notebook?)
3. Estou a escrever no meu caderno. (I am writing in my notebook.)
4. Tenho de comprar um caderno novo para o curso. (I have to buy a new notebook for the course.)
5. O caderno está cheio de notas. (The notebook is full of notes.)