I’ve never heard

Well, looks like conversation is impossible then. Unless you have better sources, those two words are not 100% the same. Anarchism is a specific word, coming from the greek anarkhia, meaning “without a ruler”. Libertarianism, on the contrary, is a more broad word, since liberta is latin for “freedom”.

The way I learned it is that anarcho-socialism is the extremist version of leftist libertarianism. A moderate libertarian doesn’t mind the existence of a government, as long as it is limited. As for the anarchists, I know that they exist and I know that there are both on the left and the right, but I don’t have interest in reading their literature (it might be a cool theory to read, but the fact that it is so far from practice makes my interest in it practically vanish).

Libertarians can be left or right. What they have in common is that the government should have limited powers, but what they disagree with is what type of limited powers it should have. Rightist libertarians believe in laissez faire capitalism (their main name in economics is Ludwig von Mises), while leftist libertarians believe that corporations should be put at more scrutiny by the government.