First off I encurage you to read the tooltips on the functions. They reveal suttle Details 
in most cases enough to figure out whats going on. (Some apply only under certain conditions!)
You have to understand there is a Priority who recives Input first or even not at all. Thats what the Input Mode is there for. (tooltip again reveals the order)
Next you have to understand that Input can be Consumed and what Bubbeling means. Each Input gets passed to someone (Controller, Character, Widgets etc.) and the one who recives the Input can decide if he wants to Consume it or not. If you Consume the input (or Handle it) that means we are done with the Input nobody else needs to recive it.
If however you decide to not Consume it (leave it Unhandled) you let the Input pass to the next one in the Priority line to recive it. That is called Bubbeling.
If you rember those Important things you should have no trouble in most cases except some Edge cases. (Third Person Click and Hold Mouse from the PlayerController for example can prevent the MouseUp event to fire in the UI)
For most UI related Events keep in mind that the Widget has to have User Focus in most cases. Since the Input System has to know to what UI we want to send the Input. You can different UI respond to the same Key but each one can do something completly different with it. Thats why we need the Focus =)
Input Event Example: Screenshot - 243253e22606d55d7a57c50c5a320a4a - Gyazo
UI example: Screenshot - e545a1d79d579652166dd959b0231118 - Gyazo