The Disaster Recovery is a plan that includes evaluating all backups and ensuring any redundant equipment critical to recovery is up-to-date and working properly. This document is a subsection of the BCP.
The Business Continuity is a plan that consists of a business impact analysis, risk assessment and overall business continuity strategy.
i.e. Your server goes down, you’d look to the DRP to understand how to get systems back online efficiently.
If the building that your company runs out of is unavailable, pile of rubble, gas leak, protest – how would you continue to conduct business if your business is unavailable. Now, part of that plan would be to implement the DRP – but what about people, chairs, computers, communication, command center, etc.