The economic axis, as represented by the Nolan Chart or other similar charts is much too simple, really, to describe the various ways in which people propose to intervene in the economy. The Vosem Chart described two different economic spectra, one for personal finances and one for corporate finances. That may not be enough. It could be up to three somewhat parallel lines, that meet at each end at the pure endpoints, but balloon outwards in the middle, giving a series of spectra that when charted looks rather similar in shape to a football. The different threads would be regulatory, ownership, and redistribution.
While there are as many ways to interfere in the operations of the free market as there are those who stand to benefit by each particular intervention, there are several basic economic systems if similarities of intervention are grouped together. These are Capitalism, Georgism, Monetarism, Mercantilism, Welfarism, Keynesianism, Socialism, Fascism, and Communism, with Capitalism and Communism comprising the pure endpoints at the extreme ends of the football spectrum.
Capitalism here represents the absence of external interventions in the marketplace. There are no regulations on what can be bought or sold, who can buy or sell it, or with what it is paid for.
Georgism and Monetarism are both "Capitalism but..." in that both allege to be basically free market systems but each believes there to be one particular special commodity that needs to be handled outside of the free market. With Georgism it is real estate, and with Monetarism it is the money supply. Georgism also has three basic varieties.
Under Taxation Georgism, a redistributionist system, the government heavily taxes all revenues from real estate, removing profit from real estate. Under Regulatory Georgism, the government controls real estate through regulation. Under Ownership Georgism, the government is the actual owner of the land. In all three the government also attempts to manipulate the use of the land, ostensibly to ensure full productive use of the land.
Monetarism, the economic system of Irving Fisher and his student Milton Friedman, has the one unique commodity being the currency. The government produces and maintains the money supply, and attempts to manipulate it in order to ensure full employment.
Beyond the "Capitalism but..." systems, there are systems that are much more heavily mixed, Mercantilism, Welfarism, and Keynesianism.
Mercantilism, also called "crony capitalism", "protectionism", and sometimes "corporatism" is technically an economic system although it lacks in the way of a theoretical basis. The state attempts to protect domestic industries from foreign competition, and promote exports and reduce imports through the use of tariffs and quotas. This can be done in terms of the general trade balance (light mercantilism) or protection of specific industries (heavy mercantilism). Some object to the use of the term “mercantilism” due to it being used to describe economic situations other than 19th century England while on the gold standard, but the basic theory (such as it is) is the same so the same term can be used.
Welfarism, simple wealth redistribution, is the opposite side of the coin from Mercantilism in that it too lacks much in the way of a theoretical basis beyond "we have to help the poor". Its meaning is obvious, but it should be differentiated from technical academically defined Socialism since that system does have a precise meaning even though the term "Socialism" is often used to describe Welfarism.
Keynesianism is a full fledged full interventionist economic system. There are no aspects of the economy left untouched by the government in an effort to achieve a productive economy. Although the initial theory is that the government should run a surplus in times of prosperity and run a deficit in times of recession, in practice all areas of the economy that are not directly part of the government are influenced by government regulation. Because it is such a sweeping system, it has several varieties and derivative systems, including supply side economics and demand side economics. Right Keynesians get along well with Mercantilists and Supply Siders. Left Keynesians get along well with Welfarists and Demand Siders.
Then there are the systems that are almost entirely government, Fascism and Socialism.
By the textbook definition, Socialism refers to the ownership of the means of production being in the hands of "the people", which in practice means the government. That really is the entirety of the textbook definition, which is why it is something different from Welfarism. That gives the government near complete control over the economy.
Fascism is actually a different system, in that instead of the means of production being owned by the government, they are controlled by the government. Given a Misean definition of ownership that includes the right to make decisions, the difference between Fascism and Socialism is "a difference without a difference" in that instead of direct ownership being socialized, merely the power of ownership is socialized.
Finally there is the other pure system at the opposite end of the spectrum. Under Communism, every aspect of the economy is owned and controlled by the government directly. Not only are the means of production centrally owned and operated, the products themselves are property of the government.
It is useful to remember to keep these separate, as there are many who would include in the definition of "Capitalism" all of those listed except for Socialism and Communism. There are nine listed economic systems, not two or three. Any attempt to obfuscate that is an attempt to lay at the feet of capitalism the faults of the other systems.