The purest form of libertarianism is anarchy, so a group of people can form a corporation and protect their collective property and wealth using force, as they see fit.
Not so. Libertarianism isn't about creating an anarchy, it is about creating and perfecting a constitutional republic based on Liberty. Libertarianism is about a free society under the rule of law which recognizes that the use of force by government is evil, but that it is still sometimes necessary in defense of that Liberty.
So put simply the difference is that libertarians seek to minimize the use of force by a government (or any collective association), while anarchists seek to eliminate the use of force by a government completely.
And what you describe isn't even anarchy which would be about having no enforceable rules. What you describe is simply creating a new government but calling it a corporation instead. As soon as you are talking about forming a corporation or association or any group of people with collective rules which can be enforced by the use of force, then you are not talking about anarchy.
Libertarianism is about some minimum set of laws which are meant to uphold individual freedom that a government may need to use force to enforce. The term "free market" refers to a market that operates by a set of rules which are collectively enforced through some government entity. The exercise of those rules and code of conduct are what make a market free or not.
So things like: you may not steel or commit theft through fraud, or threaten force to coerce someone into trading goods or services at a price that is not agreed upon fairly, those would all be legitimate things for a government to use force to counterbalance or try to prevent or punish.
Libertarianism is about minimizing the use of force by government to when it is absolutely necessary not eliminating it and certainly not privatizing the use of coercive force. Individual and collective self defense is part of living in a free society, but so is a well regulated free market which is a function of government. Without a set of enforced rules, you can have a market, but it most likely won't be a free market.
Police and common defense are usually cited by libertarians as the only legitimate functions of government power, so it is hard to see how anyone would be mistaken in believing that libertarian ideology is about creating an anarchy or would seek to allow the creation of private police forces outside the rule of law.