What is the difference between command-and-control policies and market-based policies toward externalities?

Command & Control are regulatory mechanisms. Market Based Policies are incentive based mechanisms.

Explanation:

Command & Control; Market Based Policies - are approaches used to solve the market failure from Externalities (Eg: Negative Externality - Pollution).

Command & Control : implies setting maximum ceiling limit of releasing negative externality (eg - harmful pollutant gases, here) by all individual firms. As mentioned, it has regulation in its essence.

Market Based Policies : imply setting of maximum ceiling limit for 'all as a whole' & allowing them to trade permits for releasing - harmful pollutant gases. Here; the opportunity control of each emission is - lost extra tax paid, lost subsidy, lost price at which that emission could be sold in market.

So, externality reduction in this case is not owing to any regulation, but self incentive of monetary gain in this case.