How is a ZWave Button device different from a Switch?
I am guessing that a Button device just sends a single simple command that the HE receives and is then programmed to respond to. While the Switch is designed to send preprogrammed On or OFF commands to the HE.
Is my guess correct? And if so, and all I want to do with the device is turn lights On or Off, aren't they about the same in that scenario?
A true "Button Controller" physical device cannot directly control any electrical load. They are typically battery powered devices that simply send a message to the hub indicated that a button was 'pushed', 'held', or 'released'. The hub can then use these "events" as triggers to various apps. These apps can then turn on/off other devices that are connected to the hub.
A "Switch" physical device is typically used to replace a traditional, in-wall, lighting control switch. The old switch is removed from the wall, and the new smart switch is installed. The actual electrical AC wiring is connected to this switch so that a user can still control the lighting manually, and the hub can control the lighting via Z-Wave, Zigbee, WiFi, or Lutron Clear Connect RF (depending on what switch is installed.) As you mentioned, a true "Switch" device will report its status to the hub as "on" or "off".
The most modern switches blur the lines @ogiewon elegantly described.
Both Zooz and Inovelli allow for their switch looking products to be configures as two-two-two-devices-in-one 
You install them normally and the physical paddle/toggle continues to control the load. However, by selecting the correct option, the Load portion gets disconnected from the paddle/toggle. Those become buttons, also as described by @ogiewon so elegantly.
Their Dimmers also have this separation option.
From the above responses, is it correct that Button devices are always (usually) battery operated?
Usually, yes, I'd say. I suppose most manufacturers think that if you're going to have something hardwired you might as well as least give it switch functionality, and mains power might be overkill for the average button device whose battery would probably last years.
All, no--I think Lutron has wired keypads that don't need to actually control a load (though another variation of them can). But they cost an arm and a leg I'm not willing to pay. 
(Zooz has a new "scene controller" that is a little like both rolled into one, with more buttons than a regular switch, and Inovelli is supposed to have one soon. But for the most part, I'm happy with battery devices here.)
I've used button and switch interchangeably as Dashboard device attributes when I wanted to use two different colors for similar-acting things in a dashboard (I'm too lazy to mess with CSS or whatever). No issues doing that. 
Inovelli and the newer GE Enbrighten switches are also “scene” controllers and offer button capabilities. Idea is you can double, triple, etc tap the switch to perform an action. The stick drivers for these switches include button capability.
While most buttons have been historically battery powered you are seeing more mains powered too.
Yeah, Zooz's newer ones (or any of their newish ones with newer firmware) are too. What I meant here is just that there are also distinct buttons that don't just look like a switch.
Download the Hubitat app
