Libertarian is a left-wing word.
Anarchism is a left-wing ideology.
Right-wingers stealing, appropriating and corrupting left-wing talking points to both discredit our movements and disguise the inherent selfishness of their own is nothing new. The most egregious and notorious of which would to my mind be "National Socialst" and more recently "identitarian", but still significant of which would be anarchism and libertarianism.
Anarchism is a word invented by Pierre Proudhon, the first person to ever call himself an Anarchist in 1840. A man also famous for his hottest of hot takes: 'Property is theft.'
Libertarian, in a political context, was first coined by Joseph Déjacque in 1857, a self-identified Libertarian Communist, who leveraged the term to criticise his friend Proudhon for not being inclusive enough in his perspective on Anarchism — in this context, towards the feminist struggle for women's rights.
On the other hand, the man known for coining the term "Anarcho-Capitalism", Murray Rothbard, conceded:
'We must therefore turn to history for enlightenment; here we find that none of the proclaimed anarchist groups correspond to the libertarian position, that even the best of them have unrealistic and socialistic elements in their doctrines. Furthermore, we find that all of the current anarchists are irrational collectivists, and therefore at opposite poles from our position. We must therefore conclude that we are not anarchists, and that those who call us anarchists are not on firm etymological ground, and are being completely unhistorical.'
But even were we to look beyond history towards more modern usage of these terms, all they mean, in essence, is an opposition to authoritarianism; the desire to organise horizontally, collectively, rather than vertically in a society where power is pooled at the top and leveraged against those at the bottom.
Right-wing anarchism is an oxymoron. There is no such thing. If you endorse the exploitation of the poor by the rich through heritable ownership of land and means of production (landlords & CEOs), then you endorse the legacy of feudalism and hierarchal structures. Fighting authoritarian rule in order to supplant it with a different kind of authoritarian rule isn't "Anarchy"; it doesn't matter if your goal is to replace government regulation with unchecked corporate power, replace Capitalism with one-party Communism, or take out the president of the United States in order to enforce the regime of an unelected fascist.
Anarchism is when power is equally distributed through direct democracy, and the protection of all individual rights that don't impose upon other people's individual rights. (License to kill? Not included. The right to own slaves? Also not included.)