Hello
In the MOSFET circuit, when you touch the contacts, the 0.1 µF is charged to Vcc rapidly, then the MOSFET works. After a a period determined by the 2 MΩ resistor, and the 0.1 µF capacitor, the 0.1 µF capacitor is discharged through the 2 MΩ resistor.
The same idea is implemented in the 2nd circuit, where the 0.1 µF capacitor is usually charged to Vcc through the 2 MΩ resistor, when you touch the plates, you dicharge the 0.1 µF capacitor, and the PNP darlington pair works, driving the 2N3055 transistor.
Regards