Business Continuity is another name for Risk Management

Business Continuity is sometimes called "Disaster Recovery." Disaster Recovery is an integral component of a Business Continuity plan.

In the US Federal Government, Business Continuity is known as a "Continuation of Operations Plan" or "COOP."

Contingency Management may be synonymous with Business Continuity, but in practice it is a component of Business Continuity.

Emergency Management is the municipal government equivalent to a Disaster Recovery plan; it may have some avoidance and mitigation functions.