You’re using small “l” libertarianism in an unconventional way. These days libertarianism means something more like classical liberalism. That’s why when Thomas Sowell describes himself as a libertarian we don’t assume he’s an anarchist or an advocate for socialist communes or even that his interest in liberty is strictly limited to economics.
I’ll give you credit though for making a distinction between big and small L libertarianism. Some people like to intermingle the two in order to give their arguments a little assist.
“Thomas Sowell describes himself as a libertarian”
You like lying apparently.
I don't want to pick a nit, and I would say that the concepts are much more important than the word choices, but I do not think I am using this in an unconventional way.
I have two shelves of books devoted to Anarchism. It was, at one point, a great passion of mine. The Europeans have traditionally seen liberalism as a small government position -- the Libertarian Party of the USA has (to a large extent) a the philosophy of classical liberalism. The Europeans would further say that Anarchist take a libertarian position which is a bit more extreme than a "small government" philosophy.
That's the traditional use of the terms. As I said earlier, times change and these terms morph a little as people try to finagle their positions and appeal to the masses.