Basically, DR and BC are just names or terms given to plans on how to react efficiently and systematically during when disaster happens and how to ensure the organisation continue its operations when certain functions are impeded.
As mentioned, DR is a plan that will be enforced when disaster strikes. It should state the likely problems encountered in the face of a disaster and of course the solutions. The solutions should also state the people involved and details such as when and how.
Likewise for BC, this is also a plan to ensure that the organisation continues to function in the event if someone or some key aspect of the organisation is missing. Similarly, the plan also states the problems and solutions as well as the who, when and how.
Both DR and BC may seem the same, but they are different plans. DR plans list out the solutions on how to recover from a disaster, such as where the backup systems are and how to activate them. In the IT world, it may be the necessary user IDs and passwords, and also where the backup data is and how to recover them. From the non-IT world, it may mean where the external source, such as backup power generator and how to operate it. The key in DR plans is how to recover from disaster and steps taken to revert back to normal. In BC plans, it may be a situation where the systems are taken offline, and alternative offline systems are in place to ensure that the organisation operates as usual. The key in BC plans is how to continue operations.
Both DR and BC plans have to be tested and refined so as to ensure that they are reliable. The more problems that the plans cover mean better success to recovery and continuation.