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

No.

Differences in Usage and Grammar The difference is primarily in grammar and typical usage. In Brazilian Portuguese, the gerund (desligando) is the standard way to express an action currently in progress. In Continental Portuguese, the standard construction for the continuous aspect is the preposition a followed by the infinitive (a desligar). While "desligando" is a valid grammatical form in Portugal, it is not used to express "turning off" in the continuous sense. Additionally, related vocabulary often differs, such as the word for cell phone (celular in Brazil vs. telemóvel in Portugal).

Brazilian Portuguese Examples

1. Estou desligando o computador. (I am turning off the computer.)
2. Ele está desligando o celular agora. (He is turning off his cell phone now.)
3. Estamos desligando as luzes da sala. (We are turning off the living room lights.)
4. Você está desligando o som? (Are you turning off the sound?)
5. O sistema está desligando sozinho. (The system is turning off by itself.)

European Portuguese Examples

1. Estou a desligar o computador. (I am turning off the computer.)
2. Ele está a desligar o telemóvel agora. (He is turning off his mobile phone now.)
3. Estamos a desligar as luzes da sala. (We are turning off the living room lights.)
4. Estás a desligar o som? (Are you turning off the sound?)
5. O sistema está a desligar sozinho. (The system is turning off by itself.)