For the socialist, it means outright nationalization-government ownership-of private business. In a socialist state, the government owns and operates the airlines, railroads, banks, phone companies, and any other business you can think of. Everyone is an employee of the State.
For the fascist, public or government control is just that-control, rather than nationalized ownership, via complete bureaucratic regulation of ostensibly private business.
As an ardent admirer of Marx, Mussolini coined the term "Fascism" for his brand of authoritarian, patriotic Marxism. Fascism operates under the principle of "might makes right," through the exercise of raw, naked governmental police power.
In America today, the increasingly rough-shod violation of constitutional rights by government agents in the name of "protecting the environment" or the "war on drugs" is an indication of how far we are proceeding in this direction.
Intellectually, fascism is far more dishonest than socialism, which at least has the courage to assert legal ownership of the economy and thus assume the legal responsibility for its functioning.
As we can see, liberals are the pro typical Fascist - they're dishonest and they want Government control of all aspects of our life.