There are three things that define the nature of Socialism and Capitalism which must be taken into account when discussing them.

The first is that Socialism and Capitalism are economic and political systems. You cannot have an economic system without some controls on human activity, which is accomplished through a governing body, i.e. a government.

Second, Socialism and Capitalism are also belief systems, not scientifically defined objects. Being belief systems, each has advocates and opponents for establishing or opposing them as the dominant system in a country based on their belief that theirs has the better solution for guiding the future.

Third, Socialism and Capitalism are not indivisible monoliths. Each consists of many organizational elements that can been found in just about every country now and in the past.

So, in defining either socialism or capitalism, one must recognize that they are abstract constructs, not actual things. Their image and character change through time and they overlap with each other in the same country.