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

No

While the definition, spelling, and conjugation of the verb ir are identical in both Brazilian and Continental Portuguese, the typical usage differs significantly, particularly regarding the prepositions that follow the verb and the way the future tense is constructed.

In Brazil, the preposition em (and its contractions like no or na) is very commonly used after "ir" in spoken language (e.g., Vou no médico). In Portugal, the preposition a (and its contractions like ao or à) is the standard and grammatically expected form (e.g., Vou ao médico). Additionally, while both dialects use "ir + infinitive" to express the future, Brazilians use this construction almost exclusively in speech, whereas Portuguese speakers are more likely to use the simple future tense in various contexts.

Brazilian Portuguese Examples

1. Eu vou no médico amanhã. (I am going to the doctor tomorrow.)
2. A gente vai sair mais tarde. (We are going to go out later.)
3. Você vai na festa de aniversário? (Are you going to the birthday party?)
4. Eu vou no mercado comprar leite. (I am going to the supermarket to buy milk.)
5. Eles vão no cinema hoje. (They are going to the movies today.)

Continental Portuguese Examples

1. Eu vou ao médico amanhã. (I am going to the doctor tomorrow.)
2. Nós vamos sair mais tarde. (We are going to go out later.)
3. Tu vais à festa de aniversário? (Are you going to the birthday party?)
4. Eu vou ao supermercado comprar leite. (I am going to the supermarket to buy milk.)
5. Eles vão ao cinema hoje. (They are going to the movies today.)