MOSFET Mode determination
Does the current through a resistor determine the voltage across it? Or does the voltage across the resistor determine its current? Both models are equally true, and either model could be more useful for analyzing a circuit, depending what is connected to the resistor.

One way to look at the MOSFET is that its drain-source channel is a nonlinear resistor, with an I-V curve determined by the gate-source voltage. And like any other resistor, in some cases you might want to use the voltage to determine the current; and other times you might want to use the current to determine the voltage.

It just happens that we conventionally graph this characteristic with the voltage on the x-axis (usually associated with the independent variable) and the current on the y-axis (usually associated with a dependent variable). Either way (if you included channel length modulation and parasitic resistances in your model) there would be a 1-to-1 relationship between voltage and current, and you can use the graph to find either one, given the other.