[A.J.Armitage]

The whole reason that "left wing" and "right wing" entered into our vocabulary was to differentiate between the various flavors of Socialism (e.g. Communists on one side and Fascists on the other).

Only if you consider the old feudal order of Europe socialist. "Right wing" and "left wing" come from the French revolution.

[Southack]

I'm merely referring to the "how and why" that those terms entered into common American useage.

It was to differentiate between the various wings of socialism: fascism and Communism.