The discounts are usually for business-interruption insurance. They give you a break because of your disaster recovery capability. Eventually, more and more insurance companies are going to mandate that their customers have business recovery capabilities in order to get insurance. Disaster recovery agreements and insurance policies may be triggered by similar types of events, but their purposes are completely different. Disaster recovery aims at minimizing the downtime resulting from disaster.
Insurance reimburses, or indemnifies, businesses for certain losses resulting from disasters.
Relief comes sometimes weeks, or months, or even years after the loss occurred, instead of within hours. The common law is a thicket of legal rules that have grown out of court decisions and very old laws. A good portion of the law of negligence and fiduciary responsibility, for example, arose out of the common law. And these duties can involve having a contingency plan and disaster recovery capability. That is a legal term of art that is used a lot in litigation.