Portuguese today is the fifth major language in the world. It is not only spoken by Brazilians and Portuguese but also by people from Cape Verde, Guinea-Bissau, Mozambique and Sao Tome and Principe, as well as the co-official language, along with Chinese, in Macau, and with Tetum in East Timor.
It is then, no wonder that there are differences in intonation, pronunciation, grammar rules and vocabulary for each of these countries that are so distant from each other.
Lately, though, Brazilian Portuguese has played a sort of leveling role, thanks to its world famous music and novelas, the soap operas, it exports to most of these other countries. So just like Hollywood movies made American English mainstream, novelas have had the same effect.
A difference worth noting between Portuguese spoken in Brazil and Portugal is the use of the pronouns você and tu. Both mean the 2nd person singular you, but in Brazil, tu is not as common. Você is used in all media communications and official texts in Brazil, but tu can be used in some states in the North and in the Gaucho dialect in southern states of Brazil.
When using tu the verb is conjugated differently from when você is used.
Look at these examples:
You go to school in the morning.
Tu vais à escola de manhã.
Você vai à escola de manhã.
You are a teacher.
Tu és professor.
Você é professor.
Every Portuguese-speaking country understands você, and as a learner it is easier to conjugate the verb when using você because it is the same as the one for the 3rd person singular, he/she, ele/ela.
Also, be aware that the use of tu in Brazil has some peculiarities. The Gaucho dialect, for example, spoken mainly in Rio Grande do Sul, but also Parana and Santa Catarina, will use tu but with the verb conjugated as with você.
Tu vai à escola.
Tu é professor.
Although this is limited to conversational, and informal situations, it is common.
In the Living Language Forum, I added some examples of vocabulary variation between European and Brazilian Portuguese. Most often other Portuguese speaking countries tend to agree with the European version of the language. Here are some more examples:
BP: cédula de identidade / EP: bilhete de identidade
BP: carteira de motorista / EP: carta de condução
BP: banheiro / EP: sala de banhos
Here are some examples of slight variations in spelling:
BP: aquarela / EP: aguarela
BP: caminhão / EP: camião
To learn some more differences, go to the Culture Note in Unit 3 of the Advanced book of your Living Language Brazilian Portuguese.