For a Conservative Libertarian, freedom from government regulation is an overriding value. Government measures that attempt to maximize the overall welfare of society by redistributing wealth or limiting choices are to be avoided at all costs. If the price of that is a grossly unequal society, that’s ok, because regulation is a slippery slope, governments often make bad trade-offs, and 1984 is never very far away.
CLs typically portray themselves as defenders of the Founders’ view of the Constitution as a device to limit federal power. That is patently incorrect; they are, in fact, the heirs of the Anti-Federalists, and their adoration should logically be directed at the Articles of Confederation.
Liberals, like CLs, believe in limited government, but for a specific purpose–to maximize the potential of individuals. They believe that dogmatic libertarianism in practice inevitably leads to concentrations of wealth and power that were not contemplated by the Founders. These concentrations lead to distortions of the political system, successful rent-seeking, and oligarchy. Government action is (regrettably) necessary on a regular basis to fight the natural trend towards oligarchy and to provide the less fortunate with a reasonable chance to refine and use their special talents. That, in turn, increases the overall amount of freedom (in both the positive and negative senses) and maximizes individual excellence, to society’s benefit.
The two groups see society as being a collection of individuals. As such, they stand apart from the collectivist elements (Democratic Socialists for the Democrats; Reactionaries and Christian Democrats for the Republicans) in their respective parties. The difference is that the liberals represent the majority of the Democratic Party; CLs are a small minority within the GOP.