dsp microcontroller
exactly... I think, Microcontrollers don't have hardware accelerator to do the operations which DSP does. DSPs have Multiply & Accumalte unit (MAC). But microcontrollers don't have this Unit. So the difference between these two is how fast a piece of program is executed by the processor.
And one more thing is Microcontrollers are used to do a particular task. for EX. these will be used in the application like washing machine, etc.. these microcontrollers are used in the small embedded systems.
Now a days, we have some processors which can do the work of DSP with the same or faster than & efficiently. these are ARM processors.