I have only seen one machine set up like that, an old metal planer that had been converted to a CNC mill. In that case it was a fixed gantry with a moving table. The gantry could move up and down manually with a crank for rough height adjustment. The spindle assembly was on a more or less conventional rail assembly for the main Z axis. Also consider that a knee mill has a dual Z axis adjustment, in most cases, the knee moves up & down for rough adjustment and the quill is normally the main Z axis under CNC control. I call the knee motion the ''K'' axis on my DRO.
But what to call your design? Maybe ZA and ZB Or maybe Z and ''G'' for gantry?
As far as how to build it and control it, I'm not even going to think about that.