But monarchies, aristocaracies, dictatorships, and oligarchies also control those, so how is socialism differentiated?
How many times do you need this explained to you?
Monarchy, aristocracy, dictatorship, and oligarchy describe certain kinds of political systems, without regard for the type of economic system they use.
Capitalism and socialism are economic systems, and either may exist under any of the aforementioned political systems (as well as other political systems.)
Where a country's political system intersects with its economic system is at a much more basic level. It's not about who runs the government (or who is in the government), but what rights are held by the people, to what degree those rights extend, and how those rights and commerce are regulated.