[magicalhippo]

Transistors change their effective resistance based on the "control stimulus", which in turn changes how much current can pass through them.

In BJT transistors the "control stimulus" is the current flowing through the base pin, while for (MOS)FET transistors it's a voltage potential between the gate and source pins.

The amplification happens because in the right region the change in effective resistance is high for small variations in the "control stimulus".

If you drive a BJT with a resistor in front of the base pin, you can drive it with a voltage. If you put a resistor between the gate and source pins, you can drive a MOSFET with a current source.

So the way you control them is different, but what they end up doing is the same. And by using a resistor you can effectively change the way you drive them.