Uh, no, there is zero difference between libertarians and the party they formed.
For instance this libertarian position.
“”Sexual orientation, preference, gender, or gender identity should have no impact on the government’s treatment of individuals, such as in current marriage, child custody, adoption, immigration or military service laws.””
Negative. That is the big L party’s platform. The little l position is generally “This is none of the government’s business and therefore should not be the subject of regulation.”