...those who look to the Enlightenment as the primary source of their political views, and those who look to the entire history of Western civilization, generally with a strong emphasis on the Christian era.
I think this is a better way of looking at the tension between what often gets called neo-conservatism and the various other elements of conservatism which include the religious right and paleo-conservatism. I don't have any examples at hand, but I've many times encountered conservatives who refer to "traditional values" or "Western values," but, as soon as they mention specific sources, turn out to be referring to the Enlightenment. Whereas a conservative in the second group, more often than not a Christian, is thinking of the whole Judeo-Christian tradition, and especially the past 2000 years. He may even be hostile to the Enlightenment, and certainly doesn't consider it the first glimpse of light in the darkness of history.
I believe I've seen, somewhere or other, these two groups referred to as liberty-oriented conservatives and virtue-oriented conservatives. It's unfortunate that the word "neo-conservative" has become attached to (roughly speaking) the first group, because it's a really ill-defined and loaded word, as the discussion on the previous post indicates.