Classical liberalism is a tradition of thinkers who developed an ideology opposed to politics. Political liberalism on the other hand, is a tradition of politicians (particularly from British and American liberal parties), who only claim a vague relationship with some liberal thinkers. There is little common ground between the two.
For instance, John Stuart Mill, whose works were notably influenced by his socialist wife, is considered by libertarians as a fringe author in their philosophical tradition, whereas, as member of parliament, he is considered by political liberals as a key person in their tradition. Lord Acton[?], a classical liberal author, also had some acknowledged influence on Gladstone, a liberal politician. Finally, some renowned economists and politicians in the 1920s and 1930s, such as Keynes, at the time when collectivist theories were at their highest influence, renounced to basic principles of classical liberalism while still claiming the name "liberal" in contrast with overtly collectivist economists. That's as far as the relationship goes between these two traditions.
Some try to restrict the term classical liberalism so as to stop in the nineteenth century or so. Libertarians argue that there is no interruption, no massive rejection of the past and no fork in the classical liberal tradition - only a single uninterrupted tradition, the only one which does lay claim to such theorists as Locke, Hume, Smith, Say and Bastiat, as opposed to Hobbes, Rousseau, Proudhon, Marx.
Similarly, some split classical liberalism into a political liberalism and an economic liberalism, so as to be able to consider liberal justifications of democracy independently from liberal justifications of capitalism. But libertarian thinkers themselves claim that this is missing the point, because the classical liberal tradition is neither political nor economical: it is a theory of Law - of what is or isn't legitimate for people to do.