Air Traffic Controller reported instructing an aircraft to line up and wait but two aircraft took the control instruction resulting in sending an aircraft on final around and exiting one of the aircraft off the runway.

Narrative

Around XA:10z; north operation; Runway XXL only operation; VFR weather. I had been departing aircraft with 30 miles in trail north bound for two of our departure gates the XX Gate and the XY Gate. I informed Aircraft X after departing my most recent jet that there would be a 4 minute delay for his departure for the in trail spacing. Aircraft Y checked in on final and I told him to continue for traffic holding in position. After he acknowledged; I re-scanned my flight plans and saw Aircraft Z was departing the XZ Gate which wasn't part of the in trail spacing and he was waiting at intersection 1 for Runway XXL. I advised Aircraft Z to be ready to go but I would get him out next. When I told Aircraft Z to line up and wait at [intersection] 1 he read back correctly and lined up. After he acknowledged I heard two transmissions at once and saw another aircraft further out who I assumed checked in so I reached out and told him to continue. He acknowledged and I went back to my arrival aircraft who taxied off the runway and scanned back to intersection 1 and cleared Aircraft Z at 1 for takeoff. I then cleared Aircraft Y to land; but as I was giving the clearance I saw and the CIC (Controller In Charge) saw that Aircraft X had lined up full length. I told Aircraft X to hold position at that point as I didn't want him to take off simultaneously with Aircraft Z then sent Aircraft Y around as he was around 2 mile final. Then I saw Aircraft Z still hadn't begun is takeoff roll so I canceled his take off clearance and told him to hold position. Once I had all of the read backs I taxied Aircraft Z off of the runway. The CIC coordinated a heading and altitude for Aircraft Y which I relayed and once there was adequate spacing I cleared Aircraft X for take off. I switched Aircraft Y frequency late due to everything going on but it didn't appear to cause any other issues. I don't recall any other issues/incidents after that.Recommendation:I recommend pilots confirm with ATC any instructions if there is any confusion and don't taxi onto an active runway if you're not sure. I would much rather give another transmission to avoid confusion.I also feel the constant distraction of the government shut down is effecting all incidents in the NAS controllers after a month into the shutdown with no end in sight are distracted by finances and bills that still need to be paid even though we aren't getting paid. I don't think its right to demand a high stress job of people while adding high stress to our outside lives. I suggest with the next government shutdown that all air traffic controllers and government employees be furloughed and go home until the senate/congress can do their jobs.