Given the different people and groups trying to attach themselves to the libertarian label in spite of there being no actual connection, it may seem odd to find that there are people who fit neatly within the basic definition yet often wish to deny that label for themselves. Such is the case with Objectivists.
Libertarian and Objectivist are not synonyms. That is one of the reasons Objectivists like to not use the term. Objectivism is a fairly comprehensive philosophy, touching on all five major branches: Epistemology, Metaphysics, Ethics, Aesthetics, and Logic. Libertarianism is a political philosophy, which means it exists really only within the realm of Ethics, and mostly within macro-Ethics.
Also the major concern of each varies slightly from the other. Libertarians are concerned with the relationship between the individual and the state, while Objectivists are concerned with the relationship between the individual and society. These two causes overlap significantly, but not entirely.
Even so, when a basic definition of libertarianism is given, such as calling it a political philosophy that seeks to maximize the rights of the individual, or a philosophy that objects to the initiation of force, there really is no discord between Objectivism and other schools of libertarian thought.
Objectivists try to argue that because other libertarians arrive at similar conclusions from different basic premises that the agreement is more coincidental than based on common ground. The problem with that is twofold; first it argues that agreement is basically issue specific instead of philosophy based as the two above definitions would show, and second it neglects that the basic definition of a political philosophy is based on agreement on certain core principles without regard for how those core principles were derived.
Given that second argument, Objectivists try to argue that since the derivation is unimportant it means that libertarian has no actual definition and can mean anything. That's clearly not the case given that two non-conflicting definitions were already given that effectively describe what it is to be a libertarian. The term does have a meaning, and Ayn Rand had some pretty choice words to describe those would shy away from the meaning of a word. Objectivists, if they want the term "Objectivist" to have meaning, should heed her position on the meaning of words and realize that "libertarian" also means something.
When they do admit that "libertarian" means something, then they will have to confront what it does mean. That means that Objectivists, if they are true to their philosophy, are indeed libertarians in the political sphere