I struggle to these terms of extreme left and right we so often...

I struggle to these terms of extreme left and right we so often see in the media today.

Are they Authoritarian Socialist and Authoritarian Capitalists?
Or Authoritarian Socialist and Authoritarian Religious something or other?

Often when the media talks about the extreme right Nazi come but Nazis generally were/are socialist but Racist as well.

I gather that extreme means Authoritarian the left right bit is usually a measure of government control in the economy.

Any thoughts?