Difference CPU, ASIP, DSP
"ASIP" is not a term the industry bothers to use. The similar-sounding "ASIC" (application specific integrated circuit) basically means any piece of specialized IC design that isn't a general purpose processor. 

A DSP is not "stripped down", it is optimized for digital signal processing tasks, which usually means convolution, fast fourier transform, discrete cosine transform, filtering, and so on.

This usually means having the ability to do a block of multiplications and additions in one instruction.

DSPs are generally more powerful than microcontrollers but lack some of the features required for multi-user operating systems, such as virtual memory.