“Abolition of private property” means that nothing will be owned by private individuals. While socialism is the transfer of some property to the government, communism is the transfer of all property to the government.2 Once again, this is not how communists explicitly define their ideology, but the way they do define it is effectively equivalent.
https://libertarianinstitute.org/articles/actually-socialism-is-when-the-government-does-stuff/

Of course, that is too honest to be a real Karl Marx quote.
It is a popular meme that is used to mock the allegedly misguided view of many who oppose socialism. It has been famously paraphrased by prominent socialist, Richard Wolff.
“Socialism is when the government does stuff; and it’s more socialism the more stuff it does; and if it does a real lot of stuff, it’s communism.”
These comments were made sarcastically, as socialists do not believe that “government doing stuff” accurately sums up their ideology. I intend to argue that it does.
Let me be clear: I am not proposing an alternate definition of socialism. The definitions that socialists and communists give themselves usually line up with the standard definition you can find in dictionaries and encyclopedias, and I am not going to stray from that standard definition. Instead, I will argue that their definition is synonymous with “socialism is when the government does stuff”—whether they acknowledge it or not.
For an analogy, imagine I said that I want a hollowed out half sphere made of wood (with a slightly flattened bottom so that it will stand still on a table) in which I plan to put fruit. You sum this up by saying that I want a fruit-bowl. I can protest and say that you’re putting words in my mouth, but what I described simply is a fruit bowl, and you’re not committing any kind of straw-man fallacy by telling me that.
Here is the first dictionary definition of socialism that comes up on Google: “a political and economic theory of social organization which advocates that the means of production, distribution, and exchange should be owned or regulated by the community as a whole.”
The Wikipedia definition is a little more elaborate but amounts to the same thing: “Socialism is a political, social, and economic philosophy encompassing a range of economic and social systems characterized by social ownership of the means of production, as opposed to private ownership.”
“Social ownership of the means of production” is equivalent to the means of production being “owned … by the community as a whole.”
How is something to be owned by “the community as a whole?” Ownership means that you get to decide what is done with something. If you and I disagree on who gets to eat your apple, then whatever you decide will take precedence, because it is your apple. If a “community as a whole” owns something, and two people within that community disagree on what should be done with something, who takes precedence? Whoever it is, he is the real owner of that thing, not the “community as a whole.”
Be seeing you