Does the Libertarian Party differ from other third parties?

In Downs chapter on "The Statics and Dynamic of Party Ideologies," he says that third parties in two-party systems exist for two reasons. The first, which seems more intuitive, is to come to power and at least threaten the main two parties grip on voters. The other is to influence policy. As Downs points out, clearly both these end goals require a voter contingent, but this does not mean electing officials must be the primary goal. The two examples today that clearly seem to be the latter type are the Green Party and, though not a fully separate party, Tea Party Republicans. Both of these examples reside at the edges of the liberal, conservative continuum and seem to be in place to prevent Democrats and Republicans from edging towards the median voter. While the Tea Party Republicans have gotten some officials elected, the rhetoric seems to focus on non-establishment, renewed conservative values that would limit its platform's appeal but not limit its influence on the larger Republican party.

My question then became, which type is the Libertarian Party? With no elected officials in the House or Senate and Presidential candidate Gary Johnson receiving only 1% of the vote in 2012 despite the party being formed in 1971, intuition would say the party exists to influence policy. Furthermore, both Johnson and the Green Party's Stein are likely receiving some substantial boost this election season due to the unfavorability of Trump and Clinton. Still, this answer does not seem satisfactory since its fiscally conservative, socially liberal policies take elements from both main parties (though it does emphasize reducing the government's role consistently). The fact that Johnson draws voters away from both parties backed up by FiveThirtyEight's article back in July, which found that Clinton did only slightly worse in polls with third party candidates. Additionally, Gary Johnson has been polling between 8% and 13% this election in general electorate polls with more substantial numbers in particular subsets (as high as 31% with independents, 36% with those in the military, 26% of voters age 18-29). Overall, the purpose of the Libertarian Party remains unclear and may only become apparent in future elections.