The method being talked about used to be called the "30 over" method. It came from the 'beer can cold" days. It was one of those things that got you into the ballpark for a unit you knew you would be returning to visit again soon, because a quote had to be submitted and approved for further work. Of course, proper charging for an orifice header RTU would be to use subcooling, but the method described was used, and to a limited extent, it did work.
A headmaster is a valve used to control head pressure, usually in a refrigeration condensing unit. It allows the unit to maintain temps and pressures as the system is being asked to run in low outdoor ambient temps. A change in pressure moves a pintle valve to let liquid refrigerant back up into the condenser coil, reducing its effective area, which raises pressure because it is more difficult for heat to get out of the refrigerant discharge gas coming from the compressor. You still have enough liquid for the metering device because you also have a receiver, and a correctly charged system allows for enough refrigerant to be in the coil and at the metering device in the cold weather, and to be filling the receiver in hot weather.
A Motor Master is a Carrier-branded condenser fan motor drive that controls the fan speed and operation according to condenser coil temp at a specific return bend location on the coil. This allows the device to maintain a band of temps to allow for some pressure control in the shoulder seasons of fall and spring, when you still need ac but the outdoor temps are a little low.