Voltage is allways between two points. "Gate voltage" is nothing until someone tells what is the other point. Voltmeter has 2 measuring probes for that reason.
N-channel (not NPN) mosfet gets its external control voltage between gate and source. Mosfet acts as controllable current valve. The controlled valve inside the mosfet is between drain and source.
The load is connected typically in series with the mosfet, connection at drain.
The free load terminal is connected to power supply + terminal. Mosfet's source is connected to the minus terminal of power supply. Mosfet controls how much current is allowed to flow through the load.
When one applies a control voltage, typically a few volts between gate and source (+ at the gate), the mosfet opens ad effectively the load is now connected to the power supply. Load current grows as big as the power supply voltage and load recistance allows. Load current drops gradually to zero if one reduces the control voltage gradually.
In many applications it's wanted to break the load current soon. In that case the G-S voltage should be reduced to zero as fast as possible.
Voltage between drain and source is not a way to control the mosfet. I's a cosequence "how much is left" when mosfet lets a certain current to flow thru D->S and the load takes its part due Ohm's law. Together load voltage and Vds are the supply voltage.