Disaster recovery planning is about restoring IT and communications back to full operations after a disruption.
First, the Incident Response plan responds to abnormal operating conditions to keep the business operating. The four main components of Incident Response are: Preparation; Detection and Analysis; Containment, Eradication and Recovery; and Post-Incident Activity.
Incident Response teams are typically a cross-functional group of individuals who represent the management, technical and functional areas of responsibility most directly impacted by a security incident. The team is trained on incident response and the organization’s incident response plan.
When an incident occurs, the team is responsible for determining the amount and scope of damage and whether any confidential information was compromised, implementing recovery procedures to restore security and recover from incident-related damage, and supervising implementation of future measures to improve security and prevent recurrence of the incident.
Second, the Business Continuity plan is designed to keep the organization operating through the crisis. Components of the Business Continuity plan include details about how and when to enact the plan and notification systems and call trees for alerting the team members and organizational associates that the plan has been enacted.
In addition, it includes contact numbers for contacting critical third-party partners, external emergency providers, vendors and customers. The plan provides the team with immediate response procedures and checklists and guidance for management.
Finally, when both the Incident Response and Business Continuity (BC) plans fail, the Disaster Recovery (DR) plan is activated to return operations to normal as quickly as possible.
The Disaster Recovery (DR) plan may include the following components: executive summary providing a high-level overview of the plan, department-specific plans, technical guides for IT personnel responsible for implementing and maintaining critical backup systems, full copies of the plan for critical disaster recovery team members, and checklists for certain individuals.
Terms
Adverse Events - Events with a negative consequence, such as system crashes, network packet floods, unauthorized use of system privileges, defacement of a web page or execution of malicious code that destroys data.
Breach - The loss of control, compromise, unauthorized disclosure, unauthorized acquisition or any similar occurrence where: a person other than an authorized user accesses or potentially accesses personally identifiable information; or an authorized user accesses personally identifiable information for other than an authorized purpose. Source: NIST SP 800-53 Rev. 5
Business Continuity (BC) - Actions, processes and tools for ensuring an organization can continue critical operations during a contingency. 
Business Continuity Plan (BCP) - The documentation of a predetermined set of instructions or procedures that describe how an organization’s mission/business processes will be sustained during and after a significant disruption.
Business Impact Analysis (BIA) - An analysis of an information system’s requirements, functions, and interdependencies used to characterize system contingency requirements and priorities in the event of a significant disruption. Reference: https://csrc.nist.gov/glossary/term/business-impact-analysis
Disaster Recovery (DR) - In information systems terms, the activities necessary to restore IT and communications services to an organization during and after an outage, disruption or disturbance of any kind or scale. 
Disaster Recovery Plan (DRP) - The processes, policies and procedures related to preparing for recovery or continuation of an organization's critical business functions, technology infrastructure, systems and applications after the organization experiences a disaster. A disaster is when an organization’s critical business function(s) cannot be performed at an acceptable level within a predetermined period following a disruption.
Event - Any observable occurrence in a network or system. Source: NIST SP 800-61 Rev 2 
Exploit - A particular attack. It is named this way because these attacks exploit system vulnerabilities. 
Incident - An event that actually or potentially jeopardizes the confidentiality, integrity or availability of an information system or the information the system processes, stores or transmits. 
Incident Handling - The mitigation of violations of security policies and recommended practices. Source: NIST SP 800-61 Rev 2
Incident Response (IR) - The mitigation of violations of security policies and recommended practices. Source: NIST SP 800-61 Rev 2
Incident Response Plan (IRP) - The documentation of a predetermined set of instructions or procedures to detect, respond to and limit consequences of a malicious cyberattack against an organization’s information systems(s). Source: NIST SP 800-34 Rev 1
Intrusion - A security event, or combination of security events, that constitutes a security incident in which an intruder gains, or attempts to gain, access to a system or system resource without authorization. Source: IETF RFC 4949 Ver 2 
Security Operations Center - A centralized organizational function fulfilled by an information security team that monitors, detects and analyzes events on the network or system to prevent and resolve issues before they result in business disruptions.
Vulnerability - Weakness in an information system, system security procedures, internal controls or implementation that could be exploited or triggered by a threat source. Source: NIST SP 800-128. 
Zero Day - A previously unknown system vulnerability with the potential of exploitation without risk of detection or prevention because it does not, in general, fit recognized patterns, signatures or methods.