Tower Instructor reported a conflict when an arrival aircraft lined up for the incorrect runway.

Narrative

I was training a trainee during this session. Aircraft X checked on local control frequency and reported descending to runway XX. The trainee cleared Aircraft X to land on runway XX and the pilot read back runway XX cleared to land. The pilot was inbound from the south/southeast of the airport. Aircraft Y called local control ready for departure. The trainee cleared Aircraft Y for takeoff runway XX; runway heading and advised of previously departing helicopter that was north/northeast bound. The trainee then informed Aircraft X that traffic was departing; a regional jet; caution wake turbulence. Aircraft X appeared to be joining a right midfield downwind for runway 10 prior to this and read back something along the lines of roger use caution. Aircraft Y asked local control to verify runway heading was given. The trainee cleared Aircraft Y; again; runway heading for runway XX cleared for takeoff. Aircraft Y crossed the hold short lines. The trainee turned his attention to Aircraft X to make sure the spacing looked good for them to land behind a regional jet. Aircraft X appeared to have lined up for runway Y and the trainee asked state intentions. The pilot said to land and taxi back. Aircraft X was already flared out with flaps and around 500-700 feet. I immediately took over and told Aircraft Y 'Hold position. Hold position. cancel takeoff clearance. Aircraft Y acknowledged and stopped. Aircraft X landed runway Y and I advised them to exit on taxiway 1. The trainee then advised them to hold position and issued the facility phone number. Aircraft Y was cleared for takeoff and departed without further incident. In my professional opinion the biggest safety issue was to stop the departing regional jet and avoid a NMAC. The runways are crossing and it was not advantageous to send Aircraft X around and continue with the regional jets departure roll causing further incident.Better oversight in the tower. We are currently running a rushed training program and the trainees are reaching the floor and being certified to add to staffing numbers. The tower CIC was watching a freshly rated ground controller that was having a large issue. There were two supervisors on duty at the time and neither where in the tower.