https://en.wikipedia.org/wiki/Libertarianism
“Libertarianism originated as a form of left-wing politics such as anti-authoritarian and anti-state socialists like anarchists,[6] especially social anarchists,[7] but more generally libertarian communists/Marxists and libertarian socialists.[8][9] These libertarians seek to abolish capitalism and private ownership of the means of production, or else to restrict their purview or effects to usufruct property norms, in favor of common or cooperative ownership and management, viewing private property as a barrier to freedom and liberty.”
That said, anarcho-capitalist still wants the rule of law they just don’t want to call it government. Rothbard's anarcho-capitalist society would operate under a mutually agreed-upon "legal code which would be generally accepted, and which the courts would pledge themselves to follow".[11] This legal code would recognize contracts, private property, self-ownership and tort law in keeping with the non-aggression principle.[11][12]
Anyway, Rothbard, a prominent anarcho-capitalist, states quite clearly that "libertarians" (i.e. anarcho-capitalists) are opposed to government, which contradicts your statement that anarcho-capitalists want "a strong government".
Anyway, I agree that Rothbard doesn’t want government, but I am saying he does want the rule of law which is a separation point from pure anarchism. How exactly you get a court system that’s not backed up by the threat of force without people simply ignoring it is a point of contention.
"The idea of a strictly limited government has proved to be utopian; some other, more radical means must be found to prevent the growth of the aggressive State. The libertarian system would meet this problem by scrapping the entire notion of creating a government." (The Libertarian Manifesto)