Libertarianism is the belief that the goal of civil society ought to be to maximize human liberty. What "libertarianism" looks like will differ significantly depending on how one defines liberty. There are two main traditions of thought on liberty: republicanism and liberalism. Liberalism defines liberty as lack of interference, whereas republicanism defines it as lack of domination. The opposite of freedom, according to liberalism, is interference. The opposite of freedom, according to republicanism, is slavery.
In it's most extreme form, libertarianism becomes anarchism. Liberal-tradition libertarians (descending from classical liberalism) tend towards anarcho-capitalism. Republican-tradition libertarians (descending from classical republicanism) tend towards social anarchism. Anarcho-capitalists want to abolish government and replace it with privatization of everything and pure laissez-faire. Social anarchists want to abolish government and replace it with direct democracy. These are the extremes of libertarianism, but there are many places in-between. For instance, minarchists propose minimal government rather than no government. And there are different libertarian positions as to what the role of the State ought to be (if any). There are numerous centrist libertarian positions that one could hold.
Distributism is where ownership is widespread throughout the economy, such that private-ownership of productive property is the norm for most people (e.g. that most people are capitalists rather than proletarian wage-slaves). Distributists believe that widespread distribution of private ownership is a preferable alternative to both capitalism and socialism.
Capitalism here is defined as a system with private-ownership of the means of production where ownership is concentrated into the hands of a few capitalists, who constitute a ruling class, while the vast majority of people are deprived of ownership and, therefore, must work for one of the relatively few capitalists in exchange for wages in order to survive — i.e. capitalism is a system in which most people are wage-slaves. Socialism here is defined as a system in which private property is abolished in favor of government ownership. (These definitions of capitalism/socialism are, of course, not the only valid definitions; however, these are the definitions employed by the distributists.)
Distributism is closely related to the idea of property-owning democracy, which has been advocated widely on both the left and the right. What sets property-owning democracy apart is that it is essentially republican distributism, insofar as it entails both representative democracy (republicanism) and distributism (widespread private-ownership). Distributism, in itself, can be monarchist, anarchist, aristocratic, or republican, whereas property-owning democracy refers to distributism in its republican form.
Libertarian distributism, then, is the belief that we ought to structure our society in a way that maximizes human liberty and ensures a widespread distribution of wealth. Essentially, a libertarian distributist is someone that believes that the goal of maximizing liberty cannot be achieved without first ensuring widespread distribution of ownership. This does bear resemblance to the ideas of Thomas Jefferson as well as to the ideas of
Personally, I identify as a libertarian distributist because I am a civic republican. I see property-owning democracy (distributism) as logically following from republican principles. Most classical republican theorists were libertarian distributists (although it is anachronistic to call them that, since neither term had been coined yet while they were still living). Thomas Jefferson, Thomas Paine, and countless other classical republican theorists had argued that widespread distribution of property-ownership (distributism) was necessary to secure the maximum amount of liberty possible (libertarianism). If some people have excessive amounts of wealth while others live in poverty, then it creates a situation in which the wealthy have the capacity to dominate others. Libertarian distributists believe that widespread distribution of property-ownership is necessary to minimize the domination of man over man.
My libertarian distributism is basically left-libertarian in orientation. I am not an anarchist, but I do agree with anarchists when it comes to their libertarian perspective on social issues like women's rights, LGBTQ rights, racial equality, etc. Unlike anarchists (aka libertarian socialists), I do not see collective-ownership of all means of production as the best solution to the problems of capitalism. I prefer collective-ownership for large-scale industry that requires collective labor, but smaller enterprises (crafts, trades, local stores, etc) ought to remain private. Also, we ought to encourage more small-scale private businesses and discourage big business and large-scale industry in cases where it is not necessary. Also, unlike anarchists, I do not support the wholesale abolition of the State. I believe that the welfare state is a beneficial institution and ought to be preserved. I also believe that government ought to have a role in created law and order.
A related, and corollary, concept to libertarian distributism is what I call libertarian social democracy, which is essentially social democracy re-oriented towards human liberation. A man cannot be free if he has no food, shelter, access to healthcare, etc. Freedom is meaningless if one is denied access to the basic necessities. And lack of the necessities puts one in a vulnerable position that others could use to exploit or dominate you (i.e. violate your liberty). Republican-tradition libertarianism entails the belief that society ought to guarantee a certain minimum standard to all, a floor beneath which nobody should be allowed to fall. Additionally, this libertarian social democracy would be distributist, desiring to have widespread distribution of private-ownership as the norm (rather than socialist, having public-ownership as the norm).
Left-libertarians, such as Joseph Dejacque and Peter Kropotkin, had argued that people are not entitled to the product of their labor as much as to a certain minimum standard of comfort and wellbeing. I agree with this principle, although I do not agree with the radical anarchist/utopian vision of such left-libertarians. I see libertarian social democracy with universal basic income and universal healthcare as being analogous to the sort of libertarian communism that such men envisioned. I also see it as a superior and more feasible model. In general, I have a far more conservative and republican approach to politics (though I always align more with liberals than with so-called "conservatives"). I think of libertarian distributism as being a philosophical approach or underlying philosophical framework of sorts and libertarian social democracy as being a vision for social reform based upon the principles of that underlying philosophy.