("dropper" means dropper or dispenser in what follows)

When redstone torches, dust, and repeaters power the block above a dropper, the dropper activates. When levers or buttons do likewise, a block update at y+1 from the dropper is necessary (but not always sufficient) for the dropper to activate.

Screenshot A, B, and C show setups that, when placing the torch/dust/repeater (in the powered on state) or toggling its power on from an outside source, causes the dropper to eject an item.

Screenshots D and E show a lever/button that should do likewise because they power all 6 sides of themselves, yet they do not when toggling their state.

Screnshot F shows that, when the lever (button also) is on, and a block is placed/destroyed on the dropper, it sometimes ejects an item (but only one block update max to y+1 of the dropper makes the dropper eject an item without toggling the lever/button off and on again, while also possibly needing to modify the contents of the dropper).