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

Yes

The word "muito" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. It functions as both an adverb (to intensify adjectives or verbs, meaning "very" or "a lot") and an adjective (to quantify nouns, meaning "many" or "much"). The only difference is in pronunciation:

• Brazilian Portuguese: The vowels are more open and clearly articulated. The diphthong "ui" is pronounced distinctly, and the rhythm of the word is more melodic.
• Continental Portuguese: The pronunciation is more "closed." Unstressed vowels are often reduced or nearly silent, making the word sound shorter and more compressed.

Brazilian Portuguese Examples:

1. Eu estou muito feliz com a notícia. (I am very happy with the news.)
2. Tinha muita gente no shopping ontem. (There were many people at the mall yesterday.)
3. Esse suco de laranja está muito gostoso. (This orange juice is very delicious.)
4. Eu tenho muito trabalho para fazer hoje. (I have a lot of work to do today.)
5. Ele correu muito rápido para não perder o ônibus. (He ran very fast so as not to miss the bus.)

Continental Portuguese Examples:

1. Estou muito contente com a notícia. (I am very happy with the news.)
2. Havia muitas pessoas no centro comercial ontem. (There were many people at the mall yesterday.)
3. Este sumo de laranja está muito saboroso. (This orange juice is very tasty.)
4. Tenho muito trabalho para fazer hoje. (I have a lot of work to do today.)
5. Ele correu muito depressa para não perder o autocarro. (He ran very fast so as not to miss the bus.)