Morkus from Orkus
@GMforPowergamers is correct. The result isn't what makes them the same or different. The process is. With one the task is impossible and there's no roll. With the other the PC had a chance of success and maybe even a very good chance of success and simply did poorly. They are very different even if the result is the same.In both cases the result is failure in this example.
This is true, though the bolded being from the DMG is just a guideline and not a rule.The DM is tasked with determining for all action declarations if a check of some kind is appropriate. This is just the normal process of play. Sometimes things fail outright. Sometimes they have an uncertain outcome and a meaningful consequence for failure so the DM calls for a roll.