Liberaltarianism is an ideology that combines the both ideas of Liberalism and Libertarianism. It believes in a small state and overall individualism and the live and let live philosophy of Libertarianism, as well as the ease of doing business and free market capitalism but think that complete free markets are not the way to go and aim for a more moderate view, still advocating for largely free markets, not directly Laissez-Faire. They also think that, while we have to take in consideration that not everybody can afford to pay healthcare or other necessary services in a completely private society, thus the state should try to help the worst off without actually providing the services themselves, socializing those services as a Liberal would suggest to do is not the way to go either. They're pretty much an in-between of Liberals and Libertarians, without exactly blending with either Liberalism nor Libertarianism
National Liberalism - A nationalist and more rightist version of above still cares about civil liberties and economic freedom but at the same time cares for law and order.
National Liberaltarianism - Other pragmatical Libertarian though not big fan of his redneck tendencies but I agree that nations sovereignty should be respected.
Frenemies
Social Liberalism & Social Libertarianism - You've both got some really nice ideas, although your ideal state is a little too big, and most people would confuse me with you
Social Democracy - Slow down with all that spending thing buddy.