Expanding out the names helps.
Digital Signal Processor. Exactly what it sounds like, they're designed to
process large amounts of precision data very fast.
Micro controllers, equally descriptive, they're meant for basic input such as buttons knobs dials and switches and output such as for transistor or other external device control.
As Micro controllers get faster and faster they keep adding more peripherals and instructions to the point where they're starting to blend together. A modern micro controller can do what a DSP could do a few generations ago.
And like the DSP PIC line it's basically a step outside of normal micro controller roles. I wouldn't even consider the DSP Pic line a PIC. Just like I wouldn't consider the AVR32 line an AVR.