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

Yes

The only difference between the use of "online" in Brazilian and Continental Portuguese is pronunciation. In Brazil, the word is typically pronounced with a more "vocalized" or open ending, often sounding like on-láini (with a clear "ee" sound at the end). In Portugal, the pronunciation is more clipped and follows the English phonetic structure more closely, often with a much shorter or nearly silent final "e".

Brazilian Portuguese

1. Eu faço todas as minhas compras online. (I do all my shopping online.)
2. Você está online no WhatsApp? (Are you online on WhatsApp?)
3. O curso é totalmente online. (The course is totally online.)
4. O site está fora do ar, não está online. (The website is down, it is not online.)
5. Eu gosto de trabalhar de forma online. (I like to work online.)

Continental Portuguese

1. Eu faço todas as minhas compras pela internet. (I do all my shopping via the internet.)
2. Estás online no WhatsApp? (Are you online on WhatsApp?)
3. O curso é totalmente à distância. (The course is totally distance-based.)
4. O site está em baixo. (The website is down.)
5. Eu trabalho remotamente. (I work remotely.)