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

No

While the fundamental meaning of "chegar" (to arrive) is the same, there are significant differences in grammar, preposition usage, and surrounding vocabulary.

Grammar and Usage: The most notable difference is the preposition used after the verb. In Brazilian Portuguese, it is common and natural to use the preposition em (e.g., chegar em casa). In Continental Portuguese, the standard and grammatically expected preposition is a (e.g., chegar a casa). Additionally, Brazilian Portuguese uses different syntax for questions (placing the question word at the end) and different vocabulary for objects like "bus" (ônibus vs. autocarro) or "stop" (ponto vs. paragem).

Brazilian Portuguese Examples:

1. Eu cheguei em casa muito tarde ontem. (I arrived home very late yesterday.)
2. O ônibus chegou no ponto agora pouco. (The bus arrived at the stop a little while ago.)
3. Ele chegou junto para ajudar a gente. (He stepped up to help us.)
4. Você vai chegar quando? (When are you going to arrive?)
5. A comida chega logo. (The food will arrive soon.)

Continental Portuguese Examples:

1. Eu cheguei a casa muito tarde ontem. (I arrived home very late yesterday.)
2. O autocarro chegou à paragem há pouco. (The bus arrived at the stop a little while ago.)
3. Ele aproximou-se para nos ajudar. (He approached/stepped up to help us.)
4. Quando é que vais chegar? (When are you going to arrive?)
5. A comida chega já. (The food is arriving soon/is almost here.)