Market socialism or socialism?

market socialism-Market socialism is a type of economic system involving the public, cooperative or social ownership of the means of production in the framework of a market economy.
Market socialism differs from non-market socialism in that the market mechanism is utilized for the allocation of capital goods and the means of production as opposed to government control. In simple terms, this means that all (or nearly all) firms in a market socialist country would be owned and managed collectively by their own employees

Socialism--Socialism is an economic and political system where the community or state owns the general means of production (i. e. farms, factories, tools, and raw materials.) ... Socialists believe that everything in society is made by the cooperative efforts of the people and citizens. (this is the dollar tree definition its way more complex)

Is that so?

You will always find that someone is always controlling something, irrespective of  label.

The hierarchy of natural ability, as it were.

Put two people on a desert Island and one would take control.

The level of fairness in a society, depends upon collective thinking and sensibilities contained therein.

Do you feed the poor or let them starve to death....You feed them...But you don't provide them with a luxury apartment and a Ferrari.

Market socialism.

At least it sort of works. I am a living example of this.