Tech A says that the solenoid on the starter motor switches the high current on and off. Tech B says that the solenoid engages the starter motor with the ring gear. Who is correct

Tech B is correct.

Explanation:

Generally the electromagnet for a coil of wire, which allow the  system to transform electric energy into mechanical energy is understood as a solenoid, by generating  magnetic field from electric current and induces linear motion by utilizing the magnetic field. Every modern starters depend on the solenoid to use the flywheel ring gear to enable the start drive. When the solenoid is rejuvenated, a plunger or lever is controlled which pushes the ring gear into mesh with the pinion. A standard starter solenoid has one small adapter for the starter control wire and two major terminals: one for the positive battery cable, and another one for the thick wire that drive the starter motor by its own.