Free market is run by the firms and households mainly. They control where resources are allocated, to which products production. There is minimal or no government intervention in the Free market economy. All the government can really do is policing, maximum.
Social market economy is like a combination of planned economy and free market economy, run by all three: households, firms and the government. The government has more power in this, it can do more things, it has more control. There is more government intervention in this economy than in a free market economy.
