I feel like this poster doesn’t understand what capitalism or socialism are. If by capitalism and socialism, it means neo-liberal capitalism and state socialism, then yes, mutualism and Georgism are two ideologies outside this paradigm.
Capitalism is the control of capital by single people, who pay their workers wages, while keeping the products of those workers’ labour. This divides society into two distinct economic classes, the owning class, who make their money off of people working for them, and a working class, people who are paid wages to work for said owners. In this system, owners make their money by selling said products on a free market. Beyond that, capitalism can greatly vary depending on the role of the government and other factors. Please note that markets are not capitalism! Capitalism is foremost a model of production, while markets are a model of distribution. Markets predate capitalism by hundreds of years.
Socialism is an even broader term. It is defined as worker ownership over production, essentially workers controlling the businesses in which they work. (In theory, at least.) Socialism started out as a vague working class movement, but it eventually split into three branches: state socialists, democratic socialists, and anarchists (anarcho-capitalists wouldn’t be a thing until the 1950s). Socialism should be distinguished from communism, which is an anarcho-socialist society in which money doesn’t exist and production is organised in the form of a gift economy.
You may have seen the meme ‘socialism/communism has never been tried’, generally as a form of mockery. However, this is kind of like yelling at a Presbyterian about how the Catholic church did the inquisition. State socialism is control of the economy by a government as a command economy. Karl Marx believed that state socialism would be the necessary transitionary state between capitalism and communism. Non-socialists have used the words socialism and communism mostly interchangeably for this reason, as Marxist socialism became the dominant form in the 20th century. Soviet Russia and other such countries were ideologically communist, but economically, they were state socialist (keep in mind, this is according to their own definitions). Many other socialists criticise state socialism, saying that it replicates the worker/owner dynamic, the bad part capitalism, while lacking market competition, the good part of capitalism, and any regulation by a higher authority to keep it in check.
Democratic socialists are just reformists who eventually dropped the whole workers owning the factories thing in favour of higher taxes and social spending. This is why some people may call Denmark socialist, even though they still have a capitalist economic system. A more accurate term is social democracy, named for the German social-democratic party, which split with the German communists after WWI.
Now we come to the anarchists. Though there were many precursors to anarchism philosophically, such as the Greek hedonists and Lao Tzu, anarchism as a political ideology was the brain-child of Pierre-Joseph Proudhon and Joseph Dejaque.
Both of them agreed that government and capitalism were unnecessary and ought to be abolished to create a society of total freedom and equality. However, the two men differed when it came to property and markets. Proudhon wanted market socialism, where worker-owned businesses would trade their products freely (It’s more complicated than that, but this post is already long enough). He called this system mutualism. Despite mutualism’s belief in free markets, it is still firmly rooted in socialism. Mutualist Benjamin Tucker, who ardently opposed communism and state socialism, called himself socialist. Dejaque, on the other hand, wanted a moneyless society where everything was done by each according to his ability, and given to each according to his need. This is anarcho-communism. Keep in mind that neither thinker wanted these systems imposed from above. According to all anarchists, people will naturally cooperate for the common good without being forced to do so and think crime will disappear with the elimination of poverty.
Georgism is, however, harder to classify as socialist or capitalist. In fact, I’d argue that it can be both. Georgism is, at it’s fundamental, a tax reform. Many of George’s disciples were socialists who believed in worker ownership. George himself were more ambivalent, and Karl Marx called Georgism capitalism’s last defence. I see no contradiction between market socialism and George’s ideas. Geo-mutualism is a more recent development. Geo-mutualism is essentially a mutualist form of geo-anarchism. Geo-anarchists are anarchists who want people to form clubs that will give benefits to each member, with fees being based off of land-value. Geo-mutualism is this idea along with mutualist ideas such as mutual credit and market socialism.