Neither is an exact translation. I chose "ψήφισμα" over "αίτηση", because the latter tends to mean dominantly "application" nowadays. So "sign the petition" -> "υπογράψτε την ηλεκτρονική αίτηση" would be understood as "sign the online application form" - though in a more archaic usage it is indeed much closer to "petition". I chose electronic "resolution" because the greek word includes the concept of "voting" - of something you vote (ψηφίζω) for. In fact I googled to determine dominant usage and it does turn out that ψήφισμα is used much more often to describe online petitions than αίτηση is.

The fact that the concept of a petition is rare enough to not have a standard word for it, is (I assume) indicative of something about political practice in Greece, but I'm not sure exactly what :-)

The road of excess leads to the palace of wisdom - William Blake