Hitler and Mussolini, the infamous socialists. What an insane idea. Its only claim to fame seems to be famous American conservatives who want to cleanse the image of the far-right by writing off their ideologies to the other side. It also conveniently lets everyone pretend that totalitarianism could never happen here - it's all just evil communism/socialism, and we're not doing communism here, so just trust us, y'all!
These ideologies have very little in common. While states practicing both have been heavily totalitarian, the means through which they got there, the reasoning for their absolute power and its methods of enforcement, the strength of their grip and their national ideas/goals were completely different. Trying to shove them into one box is beyond reductionism, it borders on good-and-evil storytelling where all the bad guys have a simple, one-line explanation for their badness.