My opinion on vocabulary and how it has evolved.
libertarian — Used in Europe. It originally meant “anarchist”. No government. People can function just fine without coercion. Some libertarians wanted socialist communes, and some libertarians wanted unbridled capitalism and a free market. Anarchism was a dynamic political arena, with some good ideas and some bad ideas.
Libertarian — Used in America. Third largest political party. Favoring small government. Fiscally Conservative and socially Liberal. As with any political party, there are a range of positions and no set Libertarian position on every issue. Libertarians can disagree with Libertarians on issues, just as non-Libertarians can.
Anarchism — Originally, a belief in no government. Equivalent to libertarian (see above). Today, anarchism just means Marxism. The word anarchism has been seriously debauched by the Left. They do this a lot. I have known many “anarchists” in recent years. They want big government, high taxes, lots of control so that the rich cannot be rich. Anarchists today see a great need to control people, because people make bad choices. That’s just not anarchism. It’s closer to Marxism than anything else.
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.