Business Continuity is about having a plan in place that allows your business to continue operating in the event of a major disruption. Disaster Recovery is how the IT aspect of your business recovers from that disruption or disaster (and so is a key component of your Business Continuity Plan).
A Disaster Recovery strategy will consider how long you can stand to be without access to your data or an application (RTO, or recovery time objective) and how much data you can stand to lose (RPO, or recovery point objective). Typically for core business applications there will be a hot or warm standby, which can be failed over to with no or minimal disruption, and a cold standby for data and applications that are less business critical. A crucial part of the DR and BC strategies is performing simulation exercises to validate that RPO and RTO targets are being met, and reporting accurately on the results.