Mill's On Liberty contains good examples of case-based reasoning and reasoning based on facts about human beings. Such facts are more likely to depict human nature than abstract rules based on procedurally non-conservative inquiry (e.g., Kant, Rawls, various progressivistic theories) which look at what is not the case and talk about that instead.
As Mill ably argues, freedom of opinion and fundamental liberty to choose ways of life and values which reflect human nature. We prefer them, after recognizing the relevant facts and deliberating over our desires in order to determine our preferences. Human nature is really such that these values suit it; we are such that we prefer them. This is natural law. Of course people have sometimes selected constraint over individual liberty. But such mistakes are eventually discovered via procedural conservatism: the discovery of errors about the the relevant facts or incoherence between the preference as determined and our desires. With reason's assistance we revise our preference in favor of liberty and against constraint. Hence the abolition of slavery. (There is no moral reasoning other than procedurally conservative kind, and only it can monitor its own performance.)
Of course, liberals, such as Mill, tout progress away from error toward what is preferable. This is why he recommends that conventional ways of life not be imposed on individuals but their choice of way of life should be free to diverge from convention. The trouble is that this thesis is too weak to be a real challenge to conservatism. Even Mill admits that
...people should be so taught and trained in youth as to know and benefit by the ascertained results of experience.But conservatism acknowledges and even requires that individuals should have the liberty Mill has in mind. But the traditions Mill admits should be inculcated into youth will limit their individual liberty. For they will develop preferences and habits which will persist and circumscribe the scope of any experimentation with ways of life in which they decide to partake. And in order to inculcate the traditional values Mill acknowledges, we need to judge them more worthy of inculcating than their eccentric competitors. So, their will be considerable social pressure in favor of the traditional values Mill admits must be preserved and passed on. Individual liberty must be constrained in these ways. Perhaps Mill does not see it, but he simply cannot be the free-spirit he takes himself for, given his stated commitment to tradition.
A classical liberal is simply a conservative who places more emphasis on individual experimentation with new ways of life than most conservatives do. Beyond this point lies progressivism, leftism, fascism and the other illiberal and anti-traditionalistic views. Classical liberalism, then, recognizes natural law and progress. It is not distinct from conservatism, however.