An "eswitch" is still a mechanical switch. It is normally connected and when you press it you break the connection. Compare this to the switches you are describing, they are off until you actuate them. The eswitch works by having a pin on the microcontroller grounded and once you press the switch it breaks this ground an "event" occurs. This event is what determines what the firmware does.
"E-switches" use a momentary pushbutton combined with a control circuit. The momentary pushbutton only conducts electricity while the switch button is depressed. Once the switch is released, it no longer conducts electricity. Momentary pushbuttons are mechanically much simpler than clicky pushbuttons and can be quite small with fine wiring since main current from the cell typically does not pass through the switch.
The control circuit for an e-switch is usually part of the driver firmware so is built-in to the driver. Though some e-switch lights do have a separate board controlling them and function more like clickies. With an e-switch, the driver or switch circuit remains energized. Pressing the button is simply the input the user provides to the circuit to let it know to take action as per its programming.
E-switches are capable of more sophisticated and intuitive UIs than clicky switches. Because the driver circuit in some e-switch lights is charged all the time, it can do things like time how long you've held the button on or off for example... something clicky switch lights aren't good at. This is how you get things like the elegant D4 UI. You couldn't get a UI as good as that with a clicky.
One disadvantage of e-switches is there is a small amount of parasitic battery drain even when the light is not on. This is because some power is used to keep the e-switch circuit energized.
"Clicky" switches or "mechanical" switches work differently. In a clicky, main current from the battery flows directly through the switch. When the switch is in the off position, all power to all parts of the light is cut off.
Because main current flows directly through the switch clicky switches must be heavier built (and therefore bulkier) than the momentary pushbuttons used with e-switches.
Also, clicky switches are mechanically more complex. Inside a clicky switch is a tiny rotating device that works the same way as a pushbutton ballpoint pen. This device makes it so when you press it once, it clicks to on and current stays connected even when you release the button. Press it again and current disconnects, etc.
Clicky switch lights tend to be simpler to construct than e-switch lights since it is not necessary to have a separate pushbutton wired directly to the driver. They're much simpler when it comes to building a light with a switch in the tailcap. Also, because main current is cut when the light is off there is no parasitic drain.
The disdavantage of clickies are the following:
* bigger and bulkier.
* allows for less intuitive UI
* loud click when actuated.
* less reliable and wears out faster due to extra internal moving parts.
