If we look back into the economic history of the world, we see theree possible roles for the state/ government in an economy.
i) As a Regulator: Where State takes an important economic decisions, announces the required kind of economic policies, takes the sole responsibility to get them implemented and controls and punishes those who don’t oblige with those economic decisions.
ii) As a producer/ supplier of ‘Private goods and Services: Where goods and services will be distributed among the needy according to the principles of market mechanism. Here state earnes profit as a private enterprise.
iii) As a producer/ supplier of ‘public goods’ or ‘social goods’: Where goods and services which look essential from the perspective of social justice and well being of people (ex: Health, Education, sanitation etc.) are generally distributed at subsidised prices.
[Basically whole economy pays for the cause of a few people]
As different economies select different roles for the state according to their socio- political ideologies, the world had differing ways of organising economy and resulted in the establishment of different economic system.
The economy which selected both (ii & iii) for the state under monopoly resulted in State economy. This category of economy had two variants in the Socialist economy, at least the labour was not owned and exploited by the state unlike the other- the communist economy where labour used to be under complete state control. These economies had almost no market.
The economic system which left both the roles (ii & iii) as the sole responsibilities of the private sector was called the capitalistic economic system. Here state had almost no economic role but played a passive role as the regulator.
The economic system which kept atleast one (iii) economic role fixed for the state of supplying public goods to the needy people, resulted in Mixed economic system. In some of the mixed economies the state went on to take some of the roles of supplying the private goods (i.e. ii) even by carrying a heavy burden of subsidies.