A Tower Local Controller reported non standard phraseology used by the Ground Controller led an aircraft to taxi onto a runway at the same time another aircraft was departing opposite direction.

Narrative

I heard Ground Control tell Aircraft X 'Runway XX left at Taxiway X; Tower for the back-taxi'. I was working Local Control and saw an Aircraft Y on the northwest ramp begin to taxi. I then began to scan the north end of Runway XXL and looked along its length to the south end as I cleared Aircraft Y for takeoff. 'Aircraft Y; left turn on course; Runway XX left at Taxiway Y cleared for takeoff; traffic two mile final.' Aircraft Y read back the entire transmission and then began to taxi forward past the hold line. I was then looking further to the south for any other aircraft that I might have missed on a base turn or short final. Seeing none; I turned to the STARS display to see my inbound traffic; check my sequences and see if there were any traffic conflicts. Seeing none; I turned back to the north to scan my runway again. At this point; I see Aircraft X *ON* Runway XXL taxiing southbound at a good rate of speed opposite direction and had just started to slow and turn to exit the runway at Intersection Z.I yelled to Ground Control 'That guy is on my runway!' I then tried to call Aircraft X on my frequencies but got no response. At this point; Aircraft X was crossing the hold line on Taxiway Z off the runway and Aircraft Y was on departure roll. I determined that it would do more harm than good to stop Aircraft Y departure so I let them continue. I tried to call Aircraft X again and he responded saying 'We heard you clear that other guy so we exited the runway here at Taxiway Z.'I told him that Ground Control had wanted them to CONTACT me for back-taxi; not to back-taxi and monitor my frequency. I then instructed Aircraft X to contact Ground Control on frequency again. I'm not sure if Ground Control gave Aircraft X a warning or not. I had other traffic that demanded my attention. If the Ground Controller had used proper/standard phraseology; I believe that Aircraft X would not have crossed the hold line for Runway XXL and would instead have called me on the frequency.