Yes, there is a difference between emergency preparedness and emergency management. Preparedness happens before emergency; management happens after the emergency has taken place.
Emergency planning involves organizing resources and personnel to be ready to react in case of an emergency. Different types of groups and equipment may be needed to deal with different kinds of emergency situations. Emergency planning could include creating and publicizing evacuation routes, assigning responsibilities to take care of specific parts of a community's infrastructure, and so on.
Emergency management involves coordinating all the necessary services during and after an emergency has occurred. Protecting the public, helping the injured, restoring services, fighting fires, coordinating delivery of provisions like food, blankets, clothing - those types of duties fall under the responsibility of emergency management.