Marxism is a social, political, and economic philosophy named after Karl Marx. It examines the effect of capitalism on labor, productivity, and economic development and argues for a worker revolution to overturn capitalism in favor of communism.
It is supposed to be a political and economic theory where a society has no classes. No communist system has ever had no class but has always involved oppression of one group by another.
Marxists consider the material world as an integrated whole in which all things and phenomena are interconnected and interdependent. Whereas, socialists believe in equality and abolition of private enterprise. Both require the collective to oppress the individual and when assimilation is inconvenient oppression becomes necessary even if death is the result.
The claim is that the main goal of Marxism is to achieve a classless society throughout the world. But this would mean that there are many Capitalist ideologies which would have to be eliminated before this could ever happen making all capitalist a class unto itself.