The action wizard lets you customize what happens when you, for example, press a widget or quick action button. They can be programmed to do many things.
"Device Actions" are used for triggering actions that run locally on your device. For example, Wake on LAN, opening the mouse, opening the keyboard, sending an IR signal, etc.
Note that many types of actions can also be programmed to trigger on a specific server (or active server to use the currently connected computer). This is useful if you want to control specific programs on specific computers.