I am crafting an application and cannot decide whether to use the terms Login/out or Logon/off. Is there a more correct option between these two? Should I use something else entirely (like "Sign on/off").

In terms of usability, as long as I am consistent it probably doesn't matter which terms I choose, but I did wonder about the origins of the terms - and whether one or another makes more grammatical sense. I also care deeply about the application I am creating, and want to take the time to investigate all aspects of its user experience.