Classical liberalism gave rise to modern liberalism and modern conservatism. Both of these ideologies share the basic premises of classical liberalism.
Classical liberalism is based on the ideas of limited government, democratic control of the government, individual rights, and equality for all citizens. Both modern conservatives and modern liberals believe in these ideas. Modern liberalism, then, is what you might call a "subideology" within classical liberalism. Modern liberals believe, for example, that government should be limited, but that it should be more limited with regard to laws about people's personal lives (gay rights, abortion) than with regard to economics (they are in favor of regulation of business). When individual rights and the idea of equality come into conflict, liberals would be more likely to be in favor of equality.
So, modern liberalism is one "flavor" of classical liberalism.