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

No

The difference lies in typical usage and grammar. In Brazil, "tem" is the standard, everyday way to express existence (the impersonal "there is" or "there are"). In Portugal, using "tem" to mean "there is" is considered a colloquialism and is often viewed as grammatically incorrect in formal contexts; instead, the verb há (from haver) is the natural and standard choice for expressing existence. When used to denote possession (e.g., "he has"), the word functions the same in both dialects.

Brazilian Portuguese

1. Tem muita gente na festa. (There are many people at the party.)
2. Ele tem um cachorro muito esperto. (He has a very smart dog.)
3. Tem um erro no seu texto. (There is an error in your text.)
4. Você tem o meu número? (Do you have my number?)
5. Tem comida na geladeira. (There is food in the fridge.)

Continental Portuguese

1. Há muita gente na festa. (There are many people at the party.)
2. Ele tem um cão muito esperto. (He has a very smart dog.)
3. Há um erro no seu texto. (There is an error in your text.)
4. Tens o meu número? (Do you have my number?)
5. Há comida no frigorífico. (There is food in the fridge.)