I strongly disagree with you here. The textbook definition of Fascism IS corporate control. The definition that calls Liberals Fascists is a made up one, designed only to bash and personally attack a group of people, namely Liberals. It is blatantly dishonest. If you have a beef with Liberals, then you should debate them like I do, that is, by explaining why you disagree with them.
Technically, Fascism came from the left.
And you are also wrong in dishonestly attempting to define what Liberalism is. There are actually 2 definitions: 1) Applies to those who would interpret the Constitution loosely, rather than strictly, and 2) What is known as Classical Liberalism, which applies to economics, and not politics.
Let me illustrate a difference in thinking...What is really ironic, is that conservative order promotes individual freedom, and liberal chaos reduces it.
The conservative mindset/philosophy is to seek an absolute that sets a standard. Something that is consistent across the board so that there is a defined guide from which policy, laws, etc. can be developed.
The liberal philosophy rejects a fixed, objective standard and rather goes with a flexible, floating, relativistic standard. Frequently, the law or policy is derived first and then the standard is created.
The classic example is interpretation of the Constitution. The liberal philosophy says it is a living document, i.e. the framers intent is not used to determine the meaning, rather the current desire is the interpretive factor.
Conservative philosophy goes back to what was written at the time, the debates, the rough drafts, the comments of the time to determine the original intent.
Chaos v. order, or flexibility v. rigidity. Liberal chaos/flexibility causes fluidity. What was legal yesterday is illegal today, but might be legal again tomorrow. The 2nd Amendment affirms the right of the people to keep and bear arms. Only the "people" really means the state and the founding fathers never envisioned semi-full-automatic firearms, so they aren't protected.
Versus the conservative thought that "people" means the people, not the state, and arms means arms. Not flintlocks.
The political left has also been very successful in associating the political right with nazism and fascism. If you tell a lie long enough, people will believe it. Just look at how the NAZI machine conforms to the modern left. If you take out the uniforms, the German language and the genocide (for now, lol) and you get the American left. Control of industry, schools, indoctrination of the youth, class warfare, confiscation of the property of the targeted class, etc. And do it all for the people.
Finally, in equating Libertarianism with Liberalism, you show that you have no grasp at all of what either term means.
What I said
Conservative positions should logically be called 
