If the lever is used to activate the shown circuit, then the piston will extend normally; and when the lever is turned off the piston will retract normally. Also, pressing the button will extend the piston as normal.
However, when the button turns off, the observer will output a 1-tick pulse with a slightly longer delay, as shown by the gifs, and it will quickly activate the piston.
List of power sources that act like the lever to this circuit:
Levers, trapped chests, daylight sensors, player breaking any power source
List of power sources that act like the button to this circuit:
Buttons, redstone torch inverters, pressure plates, tripwire hooks, observers (possibly), repeaters, comparators detecting signal, comparators detecting items, powered/unpowered blocks, pistons pushing/pulling redstone blocks
the button depowering is not a player input but a tile an behave differently than a player input