Thanks for your thoughts on the terminology.
However, when a CAD file WITHOUT a Coordinate System defined is added to the Map and I attempt to assign one via Catalog > Properties, the option to do that is called, "Change Coordinate System". ...But, what am I changing it from if there was nothing?
...Or, is there actually something; in other words, does ArcGIS automatically, initially, assign a default coordinate system to match the Map coordinate system or something? For example, if it was a new blank Map, then it would be WG84 Web Mercator (auxiliary sphere), so I would be "changing" it from that..?
As for the elusive PRJ file, I do not see one associated with the CAD data I have WITH geospatial coordinates. However, if I convert that to a GDB, then to a SHP -- and delete the PRJ -- then convert back to a GDB, and back to CAD -- it DOES exist. ...Any explanation for this?