What are the main differences between Classical Liberalism and Neo-Liberalism?

Classical liberalism unlike neo-liberalism is based more on the ideas of rights rather than economic prosperity. Classical liberalists focus on maximising individual freedom and on autonomy. Additionally, governments should be limited with separations of powers so that individuals can gain the most freedom that they can. Limited governments would be suitable because humans are rational and self-interested thus, ensuring that there is self-imposed regulations. One of the key ideas of classical liberalism is the social contract theory (Rousseau). This is where individuals give up some of their individual freedom by placing power in the hands of elected people (such as government officials) who work on behalf of the people. These elected officials have authority as the people have given it to them and thus are accountable to the electorate. The individual gains back their freedom when they have the power to elect a new official. The free market for classical liberals is governed by the 'invisible hand' (Smith) and thus, supports the idea of limited government.
Neo-liberalism, on the other hand, focuses more on the economics side of society rather than individual rights. Neo-liberals advocate for laissez-faire economics, which instructs that the economy is left to its own devices and is self-regulating). Neo-liberal economics focuses on deregulation and privatisation, aligning with the views of classical liberalism that a government that does not intervene is best, this is most evidently highlighted with the semi-privatisation of the Bank of England. Key advocates of neo-liberalism have been Margaret Thatcher and Ronald Reagan.