I have researched a bit and this at least fits my definition of Intarsia:
A decorative inlaid pattern in/on a surface, similar, but different than a mosaic,
made up of fitted puzzle-like pieces of wood or stone.
The word is derived from “inlay” and traces its history back to the Italian intarsia
that was likely a derivative of the Asian inlay of ivory and wood. Traditionally
most Intarsia is flat.
At some point the use of stone in Mosaic was usurped and lead to the art of stone intarsia.
A Mosaic creates an image with small pieces of ceramic, glass, or stone set in a binder.
The stones may have similar or random shapes.
Unlike Intarsia, a mosaic is made up of mostly solid color stones creating color areas that
define the pattern. The pieces are surrounded by a narrow edge of the bonding material (or grout).
Intarsia uses “fitted” pieces of stone that interlock more like puzzle pieces to create the pattern.
Variation in color is created by the textures and patterns in the stone.
Since the advent of the modern faceting machine, most intarsia is done using the indexing
and precise controls available on the machine. Faceting machine intarsia tends to straight lines
and gemometric patterns.
Traditional Intarsia - usually flat on top and precise designs -
My somewhat less traditional has a domed top - I started by calling them "composite cabachons"
so as not to upset the "true" intarsia makers.
Not quite as fancy as the true Intarisa and more freehand.
OK - that's my made-up story and I'm sticking to it!