Stupid word.
political philosophy in which the means of production are either owned or controlled by the State...or both.
Only US-Americans are thinking always (and absolutelly?) in such categories. People from other cultures normally don't do so. Most people try to find good solutions.
To be honest: I have not a big idea what are fascists. This theme always in my life had been unimportant for me. I only know Nazis.
allow the means of production to be privately owned, but controlled by the government, as it was in Hitler's Germany or Mussolini's Italy.
Nothing and everything "was controlled" in Hitler's [part of] Germany. Hitler was the darwinian law of "Hitler's Germany". I'm by the way quite sure that your imaginations about Hitler's Germany are totally different from my imaginations of Hitler's Germany. I know what it was from my German mother who had been [like] a Jew for the Nazis and from my German father who had been an Aryan for the Nazis.
A German uncle of mine ("Aryan") had been an atheist and Commie since the 1920ies and a German aunt from me ("Jew") had been a Catholic and Commie under the Russian Soviets. No one had to do anything with the Nazis from them. This Uncle was always a wonderful man full of humor so you had only to follow the sound of laughter for to find him. If you went wrong you came to my mother. By the way: He was in the 90ies when he told me he is now no Commie any longer. He was upset when he read in original protocolls what the "Socialists" had done in the GDR, the former German country from Soviets grace.
seek for the government to both own AND control the means of production,
You should slowly start to learn that words are in most cases only placeholders or empty phrases. True is what's true and god is always true and new since ever and now. You will not find the truth in words - because you will read only what you like to understand - you will find truth in your heart. So don't turn your heart into a murder pit. Give god's love a chance.
as it was in Stalin's USSR and IS in Kim's North Korea. Both systems are left-wing.
One common element between the megalomaniac narcissist Hitler, the paranoid imperator Stalin and Trump's best friend God-king Kim Jong-Un: All of them are mass-murdering tyrants. Kim Jong-Un in the third generation of criminal "pharaoes":
In a right-wing political system, the means of production are BOTH owned and controlled privately with minimum government interference or involvement.
If you say so then left-wing politics would be a politics who takes care that production also has to follow the common good and not only private interests with minimum government interference or involvement.
Your problem is what to see in "minimum". If [Deadly and/or creative] chaos should rule is your [extremist?] right wing form to think then [deadly and/or liveprotecting] law and order would be more on the left-wing side. Both forms need a lot of knowledge and intelligence and open systems.
Stalinists, Nazis - and also Islamists (Islamists are not Muslims) prefer stupid deadly tyrannies and slavish obedience.
Now go and slap your poly-sci teachers.
This is by the way a typical form how the Nazis in Germany spoke once. What you say here is it that all well educated and intelligent people should be murdered because they are your Darwinian enemies. You are not able to trust such people that when they do politics, they want to achieve the best for you and every other US-American. Is it so? But intelligence and knowledge make no one to a bad or evil human being. No one is allknowing.