Libertarianism is a minarchic philosophy. It is heavily attached to the notion of certain inalienable rights, and professes that a government's main purpose is to enforce those rights, and should be no larger than is necessary to maintain those rights in practice. As such, libertarianism is not often welcoming of government's rule in providing public goods, or regulation of commerce, because these are seen as overextensions. Like all political philosophies, there is no set point for being libertarian, rather there is just a sort of libertarian compass for figuring out if one is more or less libertarian (and this can be done on a given subject). This allows room for differences withint the category, such as some libertarian's wanting privatized roads and others wanting publics roads, or some wanting fixed currency and some not.
If you take a libertarian set of beliefs, and remove the government altogether, you essentially have anarcho-capitalism. Where the line begins and ends is not definitive, but my opinion is that when someone says police should be privatized, they are anarcho-capitalists.
That's my understanding of the subject, in a nutshell.
EDIT: I realize this can be somewhat vague because I never stated what those inaliable rights are. Well, they aren't always the same, but for a general idea, just think Negative liberty - Wikipedia, the free encyclopedia.