How to read data pertaining to running applications?
Cases 1+3 show the app is currently running; basically, both are "task manager" views.

Number 2 is rather related to "preferred apps" for a given action: if you e.g. have two web browsers installed, this decides which one is launched if you tap an URL.

Number 4 is the "application manager". Usually, an "active force-stop button" should indicate a running app which you can "kill" by clicking this; but I'm not 100% sure whether the button is always disabled when the app in question does not run.