To me it seems that there is a definite difference between simply wearing the One Ring, and wielding it as if you were the Dark Lord himself. To do the former, you might become invisible, or have unnatural age, but you are not claiming lordship over all the peoples of Middle-Earth. To do the latter (as only Sauron has done), you are openly declaring yourself as the Lord of the Rings, an act which would be noticeable to ring-bearers, Sauron himself, and other powers in Arda.
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