Short answer: they aren't. This is the musical equivalent of the fact that English has "guarantee" and "warranty" and they mean the same thing.
Long answer: they aren't. They are enharmonic equivalents in the vast majority of music that uses any of the conventional Western systems of tuning (as the author sort of goes out of their way to demonstrate in the article), and if you use or invent a different system then what you call the notes is kind of up to you since it's your system.
Long answer: they aren't. They are enharmonic equivalents in the vast majority of music that uses any of the conventional Western systems of tuning (as the author sort of goes out of their way to demonstrate in the article), and if you use or invent a different system then what you call the notes is kind of up to you since it's your system.