Re: "there is a growing desire among"
I agree with both of your comments.
Just for those lacking the knowledge:
National Socialism (nazi):
(German: Nationalsozialismus), more commonly known as Nazism, is the ideology & practice associated with the Nazi Party. (Which name they hated, btw.)
Officially the National Socialist German Workers' Party (Nationalsozialistische Deutsche Arbeiterparteior) or NSDAP.
Most definitely, socialist, but seeking the help of a deity, with “Gott Mit Uns” on the belt buckle of each Wehrmacht/ SS trooper.
"Für Ihre Sicherheit"
"For your safety"
To the original, personally, I would label them as socialist, or with socialist tendencies, but using Lenin, Stalin, Marx, etc. as examples. After all, Big Brother was modelled on that sort of behaviour, AFAIK.
As far as fascism is concerned (because that's their next epithet), that's an Italian invention, by Giovanni Gentile, with help from Mussolini.
They're all of a piece, so there's that.