The transistors both fet and bipolar have a capacity across all their junctions. it is simply the resistance of the network that is so high that makes it significant for most countries. the transistors have no inputs or outputs elsewhere. they have ports or terminals. which port will act as input and output depends on how you connect and control them.
The grid of a mos fet is separated from the substrate in which the source and the drain are constructed by a thin insulating layer. This means that under normal circumstances, no DC current can flow between the gate and the substrate / source / drain. however, since the insulating layer is so thin, the grid-insulator substrate will act as a planar capacitor.
this capacitor is actually essential to the operation of most devices and not just an unwanted byproduct. The most common type in today’s integrated circuits is the so-called improvement type. the name comes from the gate voltage increasing the conductance of the source-drain channel from practically zero when the voltage is lower than the threshold level to a finite value when the voltage is greater than the threshold.
The channel is formed by the gate voltage imposing a surface potential which will transform the semiconductor substrate under the gate into a type opposite to what it normally is. the printing of the surface potential is the result of the capacitive voltage division between the gate and the so-called depletion region in the substrate. you can imagine it in the form of two capacitors in series, the first is the grid capacity, the last is the capacity of the depletion layer.
you see, the capacity of the grid is essential. without it, there is no transistor. In fact, mosfets are very often used as capacitors in current integrated circuits.
Nowadays, gate insulators have become so thin that DC can pass through a quantum tunnel if you’re not careful.