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

No

While the word "conversando" has the same meaning and spelling in both dialects, there is a significant difference in typical usage and grammar. In Brazilian Portuguese, the gerund (the -ando form) is the standard way to express an ongoing action. In Continental Portuguese, the gerund is much less common in spoken language; instead, speakers naturally use the construction a + infinitive (e.g., a conversar) to express the same continuous action.

Brazilian Portuguese Usage

1. Estou conversando com minha mãe agora. (I am talking to my mother right now.)
2. Eles passaram a tarde conversando no parque. (They spent the afternoon chatting in the park.)
3. A gente estava conversando sobre o trabalho. (We were talking about work.)
4. Você estava conversando com quem no telefone? (Who were you talking to on the phone?)
5. Estamos conversando sobre os planos para as férias. (We are talking about the plans for the holidays.)

Continental Portuguese Usage

1. Estou a conversar com a minha mãe agora. (I am talking to my mother right now.)
2. Eles passaram a tarde a conversar no parque. (They spent the afternoon chatting in the park.)
3. Nós estávamos a conversar sobre o trabalho. (We were talking about work.)
4. Com quem estavas a conversar ao telefone? (Who were you talking to on the phone?)
5. Estamos a conversar sobre os planos para as férias. (We are talking about the plans for the holidays.)