I've always used the term "musical" as a grouping for the various distortions that occur in a product. You have harmonic distortions, phase distortions, intermodulation distortions [blah, blah, blah] -- some of these distortions can leave a very pleasant [musical] set of artifacts, others - not so much.
Its a term I use when I'm either being lazy or realize that my "in-depth" explanation will go zooming over the head of the person to whom I'm responding [which I suppose is another form of "lazy"].