Karl Marx distinguished between private property and personal property in several key ways. According to Marx, private property refers to the means of production (such as factories, land, and machinery) that are owned and controlled by a small group of capitalists, who use these resources to exploit the labor of the working class.

Personal property includes possessions such as homes, clothing, and consumer goods, which individuals use for their own personal use and enjoyment.

Generally only an American idiot uses the words equality and Marxism in the same sentence.  Marxists advocate for the elimination of private, not personal property.  This is misconstrued into thinking Marxists want to equally distributed wealth by trolls and others.

In a communist society money is eliminated.  But that will never happen.  Communism is an unobtainable ideal.  It is only the direction to move to, subject to the constraints of of actual material conditions.

I have a retirement account.  My retirement account is PERSONAL property.  My House is PERSONAL property.  There has been no free money given to me. I earned all of mine.

Marxism does not advocate for brain dead, across-the-board equality.  An equality where everyone has exactly the same wealth. Instead, Marxism eliminates fundamental inequalities arising as a contradiction in and from the capitalist system.  A small capitalist class owns the means of production and exploits the labor of the working class.  A small capitalist class makes all decisions and the mass of humanity must abide by their decisions.

A small capitalist class is committed to making the mass of humanity extinct.

Many philanthropists of the ragged pants distort the reality of Marxism into 'making everything equal'.  They fear Marxism will interfere with their god given right to give the rich everything. 

And they are not wrong about that.

*  Marx, Lenin, and Mao all acknowledged the distinction between private and personal property.  With each proposing different approaches to property ownership based on their respective revolutionary theories.

QuoteThe distinguishing feature of Communism is not the abolition of property generally, but the abolition of bourgeois property. But modern bourgeois private property is the final and most complete expression of the system of producing and appropriating products, that is based on class antagonisms, on the exploitation of the many by the few. -- Karl Marx