The drain characteristics of a MOSFET are drawn between the drain current I_D and the drain source voltage V_DS. The characteristic curve is as shown below for different values of inputs.

Actually when V_DS is increased, the drain current I_D should increase, but due to the applied V_GS, the drain current is controlled at certain level. Hence the gate current controls the output drain current.

Transfer Characteristics

Transfer characteristics define the change in the value of V_DS with the change in I_D and V_GS in both depletion and enhancement modes. The below transfer characteristic curve is drawn for drain current versus gate to source voltage.