You may have noticed some similarities between Azadism and other existing economic philosophies There is indeed a bias towards one side over the other in the debate between Capitalism and Socialism, however Azadism has unique and specific traits of its own encapsulated within it's definition Let's observe these similarities and differences below...

Definitions below are from the Oxford Dictionary

Socialism

Def

A political and economic theory of social organization which advocates that the means of production, distribution, and exchange should be owned or regulated by the community as a whole.

Socialism vs Azadism

Historically Socialism has been widely understood by economists to refer to the increase in state intervention in a nation's economy. Most criticism of this idea has stemmed from this common understanding of the phrase. However, recently with the emergence of the modern "Left", those traditional views of socialism have become confused. The Oxford dictionary definition, further adds to this confusion by broadening the definition to accommodate current attitudes. Azadism does not have a problem with the "means of production" being owned or regulated by the community provided this is done privately, absent of force and coercion by a state government. As long as this is done through voluntary participation, an Azadist system can house many socialist communities within the wider Azadist framework. For example, there is complete freedom for communities to come together and set up worker co-ops or community hospitals and services, provided that participation in these ventures are voluntary and not funded through forced taxes. Therefore, Azadism is against 'State Socialism' specifically.

Communism

Def

A theory or system of social organization in which all property is owned by the community and each person contributes and receives according to their ability and needs.

Communism vs Azadism

Communism is another idea of social organisation where the community as a whole owns all the property, rather than each individual themselves. The problem here is that this community is likely run by a group of representatives, so it is essentially the government owning and controlling the allocation of resources. This is historically how it has been expressed in places like the Soviet Union and Maoist China. As a result, Azadism views this as a complete erosion of human freedom, since everything would have to go through the state in order to be approved. Azadism instead gives each individual their own personal freedom over their property. If people want to organise themselves in a Communist fashion, then even under Azadism they are free to do so as long as admission into and departure from these communities are unrestricted. In other words, as long as all participating are doing so voluntarily, then communes and individual non-state entities are free to exist under Azadism. Karl Marx's original ideas however are at odds with many of the principles on which Azadism stands on, hence why similar to Socialism, it should not be implemented at a national level. A future post may go into the exact differences, as well as the '10 planks' he outlined in his manifesto.
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In the meantime, please see Jordan Peterson's excellent critique of the Communist Manifesto here

Capitalism

Def

An economic and political system in which a country's trade and industry are controlled by private owners for profit, rather than by the state.

Capitalism vs Azadism

If you have read the Manifesto and been through the notes, you may have picked up on the similarities between Azadism and Capitalism. This is no coincidence since Azadism is inherently a capitalistic idea with a few specifics embedded into it. The reason why this was not made clear from the beginning, or why you will find no reference to the word "Capitalism" (except for the notes) in the Azadist Manifesto is precisely because most people are clueless. Since the word Capitalism is so demonised amongst the young generation of today, it was pointless using this in the Manifesto since it would have automatically triggered a negative response from many. In reality, most of these people don't understand what Capitalism even is to begin with and often conflate it with ideas such as Corporatism, Cronyism and Consumerism.
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However, the key difference between the Oxford definition of Capitalism and Azadism' is the point about profit. Although making a profit in any system (even non-economic related) is common sense for the continuation of any project or venture, it is still not a necessity. Private owners in an Azadist system do not have to make financial profit their sole purpose (e.g. charities, religious institutions, family etc). Azadism also incorporates a Khalsa government system to help facilitate the process of becoming more economically free. Apart from this, the rest of the definition of Capitalism is consistent with Azadism.

Anarchism

Def

Belief in the abolition of all government and the organization of society on a voluntary, cooperative basis without recourse to force or compulsion.

Anarchism vs Azadism

Anarchism is the extreme capitalist position, where the state is completely removed altogether. This is the ultimate long-term vision of Azadism, however, as of writing this, humanity doesn't seem to be ready for a system like this in the author's opinion. Instead, a better strategy may be to reduce the size of the state first and then experiment with this at a later stage. This idea shouldn't be confused with the modern leftist version of this, as we will see below, this often tends to be a paradoxical position for many who claim to be both socialist/communist and anarchist. Instead, the Anarcho-capitalist position is more consistent. For those concerned about how vital functions of society can be upheld such as security, then please read Chaos Theoryby Robert P Murphy for a more comprehensive outline.

Free-Market

Def

An economic system in which prices are determined by unrestricted competition between privately owned businesses.

Free-Market vs Azadism

Free-markets are incorporated within Azadism as a vital component of economic freedom. The only restriction of a free market under Azadism is when the trade of a certain good or service breaches the Non-Aggression Principle.

Where does Azadism sit on the Political Compass?

The Political Compass aims to show the full spectrum of both Political and Economic ideals. The Left-Right axis signifies the economic scale (more socialist = further left, more capitalist = further right), whereas the Authoritarian-Libertarian scale indicates a social scale. The further north you go on the compass, the less freedom each individual has, and more the power the state has.
Starting from the top left, the 'Authoritarian Left' quadrant includes ideologies like Communism, where the state has more control over a nations economy and politics the further north-west you go on the compass.
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Alternatively, the bottom right 'Libertarian Right' quadrant wants the opposite - less state control and more individual freedom the further south-east you go. The extreme of this position is Anarchism.
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The Authoritarian Right is where most western nations sit. They promote greater state power whilst simultaneously promoting capitalism. The problem with this however is that it is a self-contradicting position. You can not on one hand say you want more private (non-state) control over the nation's trade and industry, whilst at the same time wanting to increase government influence. Capitalism as an ideology, trends towards the bottom right, not just the right. Therefore, this is position is nonsense and it is evident to see the scale of damage that occurs as nations exist here.
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The Libertarian Left is similarly another nonsense position. You can not promote socialism on a state level whilst also maintaining individual freedoms. For example, if a socialist wants the state to nationalise healthcare, this pushes them towards the Auth-Left quadrant, not Lib-Left. The common counter-argument then to this is that Lib-Left want the "community", not the state, to take over. However, this is the definition of a state:
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"a nation or territory considered as an organized political community under one government."
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If they then argue that there is no "one government", then who enforces the socialist projects? What happens if one community does not want to organise a particular enterprise as a worker co-operative? What about if someone wants to do something on their own? If the answer is the whole community controls it, then this is a government and they are promoting the state. If each person is not free to organise or command their own property of their own accord and instead it is the community as a whole which decides, then each individual is a slave to whatever political system is in place that determines their fate.
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However, worker co-ops and socialist communities that are not imposed at a state level are able to exist within capitalism. If a group of individuals come together to open a socialist healthcare system, then this is completely fine so long as all agree to participate voluntarily. Socialism on a state level is anti-freedom, anti-libertarian and anti-Azadism. But socialism done privately and voluntarily on a community level is just another form of organisational strategy alongside autocratic firms, non-profits, charities, sole traders, etc.
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Therefore, on deciding on a set of policies or economic beliefs to apply at a national level, only the Auth-Left and Lib-Right positions make any sense. The chart below better visualises this spectrum for the state level.

Anarchism is the complete removal of all state and government in a society. This is complete individual human freedom unaffected from any interference from public governments. Any sort of governance exists entirely privately and voluntarily as per each individual's own choice to participate in or not. The opposite extreme is Communism. This is the complete removal of all private property as the state maintains all control over every aspect of an individuals life. This includes housing, work, food, family and even religion. All other consistent ideologies and individual beliefs, such as Ayn Rand's Objectivism, Milton Friedman's policies, Maoism, Leninism, Reaganomics etc., all exist between these two points - including Azadism. The more something trends towards Anarchism, the more capitalistic it is. This includes more individual liberty and freedom, more privatisation (handing over industry to the people instead of the state) and fewer taxes. The more towards communism you go, the more state-level socialism a society adopts and as result higher taxes, more nationalised industries and authoritarianism to the point of totalitarianism.
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Azadism exists towards the left-hand side of this scale with its tendency to reduce state control. An Azadist society begins when the state is responsible for the following 4 functions only:
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1. National Defence

2. Policing

3. Justice System

4. Tax administration
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The more towards anarchism the Azadist Nation trends, the more Azaadi it has until it reaches full Anarchism - i.e. a society becomes Azaad. Since Azadism is a general trend towards more liberty, it occupies a range on the above scale, rather than a specific point. Other factors that define what counts as an Azadist system or not is the topic of the Azadist Manifesto.