Many see socialism as the cure for inequality, a system where the wealth gap wouldn't exist. Those are the common talking points because they're effective and take away from the actual goals and affects of socialism.
Socialism is a political, social, and economic philosophy encompassing a range of economic & social systems characterized by social ownership of the means of production & workers' self-management of enterprises.
Venezuela is more equal than the United States. However in Venezuela, 96% of the people are poor, and 70% live in extreme poverty. Is it a more 'equal' country technically? Yes.
The trickle-down "theory" states that tax cuts for businesses and the wealthy will generate prosperity at the top that will eventually "trickle-down" to everyone else.