What is the difference between left and right wing schools of thought?

This question and answer are to be taken as a general rule of thumb. It is important to bear in mind that due to huge variety of political ideologies on the spectrum, there are always exceptions to the rule (such as Thatcher's social policies, which saw an increase in state powers over education despite the commitment to rolling back the frontiers of the state).

The most fundamental division between left and right wing ideologies focuses around two key issues, the role of the state and the economy.

Right wing ideologies stem most prominently from classical liberalism and the idea that the individual is the most important aspect of society and their freedoms should be protected (also that inequality is natural due to the differences of people at birth e.g. smarter or more entrepreneurial).

This means that right wing ideologies tend to be sceptical of the state and argue for the limiting of it's powers, for example in social policy. They argue this is important in order to ensure that the state does not infringe on the personal freedom of it's citizens. A good example to use here is Margaret Thatcher's reforms in the UK in which she talked about "Rolling back the state". 

This also means that right wing ideologies tend to argue for less regulation and fewer restrictions to the economy. Friedrich Hayek, an Austrian economist, was a pioneering figure in this field in his work 'The Road to Serfdom', in which he argued strongly for laissez-faire economics over more interventionist states, attacking the latter as totalitarian.

Therefore, the two key features of right wing schools of thought are a suspicion of the role of the state (resulting in a smaller state model) and a preference for market-based economics.

For left wing ideologies, a great deal of political thought on this area stems from Karl Marx with his two famous works 'The Communist Manifesto' and 'Das Kapital'. Left wing thinkers argue that inequality is a bad thing as our outcomes in life are only a product of the circumstances we are born into, and therefore it is not someone's fault if they are poor as it is likely their parents were poor before them and they had limited opportunity to improve their situation.

As a result of this left wing schools of thought argue for a larger state that can provide welfare and various public goods such as the National Health Service in the UK for it's citizens. In the past certain state's have also been significantly more authoritarian (although this should not be mistaken as a trait of all left wing states) such as Stalin's USSR, in which personal freedoms were heavily limited in an attempt to promote work as the key expression of one's personality and pleasure.

As well as this, left wing ideologies tend to propose more regulation in economies or even planned ones, as they believe that market's tend to be self-serving and are not in the interests of the populace as a whole. There is a great deal of debate here between different schools as to how much regulation a state should impose, with certain governments enacting a complete planned economy with all aspects of industry being organised by the state, and other governments pursuing very limited levels of regulation such as the Blair government from 1997-2007. However, it is safe to argue that more left wing ideologies propose greater levels of regulation on the economy.

Therefore, the first key feature of left wing schools of thought are a commitment to a larger state to provide public services to it's citizens such as welfare, health and education. The other feature is a general belief in greater levels of regulation to the economy in order to ensure that industry and the market serve the interests of the people rather than private business owners.