The best way to get at the distinction that you have in mind, I think, comes from a term I saw sometime back that might encompass what people think of as "neocons" and the "Christian Right". These are generally the groups that are distinguished from libertarians and the term I saw used was "pro-government conservative". That is, the political atmosphere in America seems to be that the Republican Party ("conservatives") have moved away from their previous positions on states' rights and government size/scope in favor of issues like international hegemony, increased military spending, and government regulation of morality. That is not to say these blocs have sworn off "small government" but rather that it's taken a backseat in priority to these other things. There, I believe is the distinction you're seeking.

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"Government big enough to supply everything you need is big enough to take everything you have... The course of history shows that as a government grows, liberty decreases."

-Thomas Jefferson