European Portuguese and Brazilian Portuguese are the same language. The difference between them is similar as the difference between American English and British English, for example, or between different regional dialects. In writing, the differences are mainly in vocabulary – for example, there are different words for the same concept. However, they are easy to understand according to the context. Pronunciation can be tricky, especially for Brazilians understanding people from Portugal, but it is a question of getting used to it.
An important difference is the way to address people. In Portugal, you can address people you know very well (like friends and family) in the second person singular (“tu”) and people you don’t know very well (like people you just met or people at work) in the third person singular (“você”). In Brazil, you do not address anyone by “tu”, it can be considered rude.
Another difference is that in Portugal you can use the gerund (“estou estudando”) or (usually) a + infinitive (“estou a estudar”) whereas in Brazil you usually only use the gerund.
Here is a list (not exhaustive) of different words for the same concept: