What is the difference between liberalism and neo-liberalism?

Neo-liberalism is the economic subset of liberalism. Liberalism is a political theory about all aspects of society - human nature, the role of the state, freedom, equality, the economy. Neo-liberalism is liberalism's capitalist view of the economy and the role of the state in managing the economy.
A neo-liberal would argue that the best sort of economy is a free market - that means that the government ought to have minimal, or even no, intervention in the economy because of the 'invisible hand' (Smith) of the market. This is the view that the market is a self-regulating and self-perpetuating entity that works best when left to its own devices. The free market can be contrasted with a planned economy. A planned economy, supported by leftist economists (socialists/communists) is the idea that the government ought to intervene in the economy for maximum efficiency.