If the outcome would be the exact same.... then there is no socialism. Free Market Capitalism, is just that.... free market capitalism. There is no socialism involved.
You can't have it both ways. It either is operating like a market, or it is not. It can't be both.
Don't you understand the basics of political economy? Factors of production are treated as independent of the market. Market socialism simply means that factors of production are organized socially as opposed to free market capitalism where the factors of production are owned and organized privately. Regardless of the way in which you organize the factors of production, the products can still be sold in the market.
But that simply isn't true. You are acting like the factors of production, are separate from the market.
If you control how "way in which you organize the factors of production" then that isn't how the market would have them. That's socialism, and doesn't work.
That has a huge effect on production.
Let me give you a simple example:
I looked up the cost of building and starting up a restaurant, like any fast food place. The startup costs were between $2 Million to $3.5 Million dollars.
Let us say for the sake of argument, that the cost to build and open a new store is $3 Million.
Now according to your own words, you said "factors of production are organized socially as opposed to free market capitalism where the factors of production are owned and organized privately".
Under your system, why would I invest $3 Million into a store, that in the end, I don't own? Well I would not. Honestly, I could invest that $3 Million dollars in the stock market, and get a 10% return, for $300,000 a year in income, and that's doing nothing at all. Don't have to deal with employees, or bills, or angry customers. So I'll invest that money into stocks, before I build a store, that you take ownership of it away from me.
Now that does not mean that I don't build the store. I will still build the store, just not in that country. I'll find another country to invest my money into building a store.
What this is called in economic terms is "Capital flight"
https://www.miamiherald.com/news/nation-world/world/americas/article1954791.html
This is a perfect example:
Not only has money failed to come in, but Barclays Capital, an international investment bank, estimates companies have taken some $150 billion out of the country since currency exchange controls were instituted a decade ago. In part, they were supposed to prevent capital flight. An average of $20 billion a year has been sent abroad over the past five years.
In recent years Venezuelan companies have invested $920 million in the Dominican Republic, according to the Dominican Republic Export and Investment Center.
Although the Cisneros Group still has substantial holdings in Venezuela, it moved its operational headquarters to Coral Gables (Florida) in 2000.
A 2009 diplomatic cable released by WikiLeaks, stated the principal owners of the company, the Cohen family, were “ready to negotiate, to give the government what it wants … but no one will talk to them,’” a lawyer who represents the family said, according to the cable.
The diplomat who wrote the cable added, “The Cohens were losing money because of the delay … and planned to concentrate new investment outside Venezuela.”
Now no doubt in the ultra short term, having "factors of production are organized socially" will reap results. In the short term the cost of food went down in Venezuela. In the short term, housing became affordable in Venezuela. In the short term, things will improve.
But in the long term, controlling the 'factors of production' to be organized 'socially', will destroy the reason for investment. The result is capital flight.
Multinational companies are dumping their Venezuela operations in fire-sale deals
Companies will sell off their operations, and reopen their operations in other countries. The result will be massive job loss, production loss, and poverty and decline.
So to recap everything in the simplest terms.... 'market socialism' is just socialism. And it does not work.