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

No

While the spelling and literal meaning of "adorando" are identical in both varieties, there is a significant difference in typical usage regarding the continuous aspect. In Brazilian Portuguese, the gerund (adorando) is the standard and most natural way to express an action currently in progress. In Continental Portuguese, while the gerund is understood, it is much more natural to use the construction a + infinitive (a adorar) to express the same ongoing action.

Brazilian Portuguese Examples

1. Eu estou adorando este filme. (I am loving this movie.)
2. Ela está adorando o presente que ganhou. (She is loving the gift she received.)
3. Nós estamos adorando as férias no Rio. (We are loving the holidays in Rio.)
4. Você está adorando a comida? (Are you loving the food?)
5. Eles estão adorando a nova casa. (They are loving the new house.)

European Portuguese Examples

1. Eu estou a adorar este filme. (I am loving this movie.)
2. Ela está a adorar o presente que recebeu. (She is loving the gift she received.)
3. Nós estamos a adorar as férias no Rio. (We are loving the holidays in Rio.)
4. Estás a adorar a comida? (Are you loving the food?)
5. Eles estão a adorar a casa nova. (They are loving the new house.)