Dual processor means two processors are available with motherboard for doing multi-threading ,multitasking or perform other processing.For example we can say two separate processors as in a dual Xeon or Opteron system.
But Dual core processor has single processor with dual(two) cores for example in a Pentium-D ,Athlon64-X2. It will perform the task also multithreading etc.
Dual core processor is cheaper then dual processor because dual processor will take two CPU that will costly compare to single CPU with two core processor.