Ayn Rand describes it fairly well. The differences are in operation:
The main characteristic of socialism (and of communism) is public ownership of the means of production, and, therefore, the abolition of private property. The right to property is the right of use and disposal. Under fascism, men retain the semblance or pretense of private property, but the government holds total power over its use and disposal.
Under fascism, citizens retain the responsibilities of owning property, without freedom to act and without any of the advantages of ownership. Under socialism, government officials acquire all the advantages of ownership, without any of the responsibilities, since they do not hold title to the property, but merely the right to use it—at least until the next purge.
The end result is the same though.
In either case, the government officials hold the economic, political and legal power of life or death over the citizens.
https://www.google.com/books/edition/The_Ayn_Rand_Lexicon/7syA3yAPsNkC?hl=en&gbpv=1&pg=PT213
Getting back to the topic of the OP, Woodrow Wilson is an interesting case but also a proof of concept about the details of progressivism. This causes a lot of confusion among many. "Progressives are communists!" "Progressives are fascists!" To some extent, they're neither while at the same time they are both. A chameleon will be whatever it needs to be.
In the case of Wilson, on the one hand he expanded on Theodore Roosevelt's regulatory state and developed it into the full blown all-encompassing regulatory state that TR dreamed of - it engaged in a scheme of centralized planning without direct ownership. To that extent it's fascistic except in reverse. Fascism hadn't been invented yet and was kind of still percolating on Syndicalism and Hegelianism in the days that TR was expanding government. So it can't be that simply by looking at a calendar.
While on the other hand, Woodrow Wilson nationalized the trains, establishing direct and unquestioned control and ownership.
You could say that progressivism unites fascism and communism, but that really doesn't properly capture the situation because you then have that whole "Red Scare problem" you have to deal with that the Wilsonians conducted under the leadership of Palmer. Progressives are not communists and when it suited them, turned on them with the snap of a finger.
Progressives really don't care about all of this rigidity and are infinitely malleable, whereas the fascist is rigidly fascist for the sake of it and the communist is rigidly communist for the sake of it. Progressives are chameleons who will work with anybody in order to get to the next step. They do not care. All that matters is government. Singularly, ultimately, government. Everything else is fungible. That's their one and only single ideological rigid bullet point: government. They don't even need regulatory agencies that actually do anything, the agencies just have to exist. Progressives can empower the agency later and if it becomes too scandalous, remove power so that it can be re-powered later. Sure they will whine like no other at the prospect of de-regulation, but de-regulation is only a setback, that's only a speedbump. Abolitionism is death. Note that in the 120 years since Progressivism came into existence, not one regulatory agency has ever been abolished. Progressivism unlike communism and socialism and fascism has a 100% successful track record. It breaks my heart to say it, but I don't know what else to say or how else to say it. Can you point to any one that ever got abolished? I can't. Maybe a small handful of wartime agencies here and there, that were never intended to have a long life anyways. We have got to start abolishing agencies whole.
You want to talk about the immortality of progressivism? Let's talk about the FDA. Let's talk about all of the land grabs that became our "national parks", the EPA, the USDA, both of the DoEs, OSHA, FCC, FAA, DOT, HHS, TSA, CFPB, IRS - it's impossible to name them all. Communism does not have a track record this pristine. No way! They cannot compete and it isn't even a question the winner here. In 120 years, progressives have proven to be untouchable.
The best thing we can do is cast progressives as progressives instead of trying to re-cast them as something else. That's not what they are. Heck, they spent the last 80 years not even calling themselves progressives, they called themselves liberals! They don't even care about what they are called, they just care that government grows. That's it.
When the Wilsonians were out there throwing communists and socialists into prison, they didn't do that because of their undying love of Karl Marx.
At the end of the day though, understanding Woodrow Wilson and Theodore Roosevelt are firm requirements to understanding the despotism that progressivism presents. Without these two, none of it makes sense. At all times in progressivism's existence, the watch word is "expert". That's who lives in these bureaucracies and that's who lords over you and I. The "experts". They can't chameleon their way out of this one and they don't try. It's their signature and it's as clear as day. The challenge is, some people will see the chameleon, and some people will see what the chameleon is hiding itself as. Rand also wrote in the same link above:
The fascist-Nazi axis scorns material comfort and security, and keeps extolling some undefined sort of spiritual duty, service and conquest.
The progressive doesn't scorn material comfort - progressives promote it heavily under the guises of either "equality" or "equity" - nor are any of those three extolled. At least, not primarily. The progressive extolls expertise. Under TR, it was the experts. Under Wilson, it was the experts. Under FDR, it was the experts. Under LBJ, it was the experts. Under Nixon, it was the experts. Under Bush, it was the experts. Under Obama, it was the experts. Pick any one of them - Bush, Wilson, Clinton, Carter, any one you want. It's always the experts and it's the experts right now. Why would anybody ignore this?
It’s a good analysis about the perpetual motion machine that is the regulatory state — and, I would add, the “expert” class, which merely moves on from one problem to the next without ever fixing anything (generally causing the next problem).
As a teacher I can tell you about the endless stream of “new” strategies and policies, none of which do any good. Apply that to general governance and we’ve got a serious problem.
As for progressivism/ nazism, communism... it’s all totalitarian and operates on the same fundamental principle of disallowing dissent. We’ve so far held out against its worst eventualities through our constitutional protections, as tenuous as they are, and the federal structure, which has largely managed to hold the worst of the Leviathan at bay.
XVI. Will the peaceful abolition of private property be possible?Given this outlook, then there really is no difference between fascism and communism; the former is merely Lenin’s New Economic Policy under a different name.
It would be desirable if this could happen, and the communists would certainly be the last to oppose it. Communists know only too well that all conspiracies are not only useless, but even harmful. They know all too well that revolutions are not made intentionally and arbitrarily, but that, everywhere and always, they have been the necessary consequence of conditions which were wholly independent of the will and direction of individual parties and entire classes.
But they also see that the development of the proletariat in nearly all civilized countries has been violently suppressed, and that in this way the opponents of communism have been working toward a revolution with all their strength. If the oppressed proletariat is finally driven to revolution, then we communists will defend the interests of the proletarians with deeds as we now defend them with words.
XVII. Will it be possible for private property to be abolished at one stroke?
No, no more than existing forces of production can at one stroke be multiplied to the extent necessary for the creation of a communal society.
In all probability, the proletarian revolution will transform existing society gradually and will be able to abolish private property only when the means of production are available in sufficient quantity.
— The Principles of Communism