Sam was new to posessing the ring, Frodo had carried it for thirteen months. So Frodo resistance wore down over the months, while Sam only had it for a couple of hours tops.
As for Sam wearing the ring in Mordor, I don't know how Sauron could have missed him.
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I heard the bells on Christmas Day. Their old, familiar carols play. And wild and sweet the words repeatof peace on earth, good-will to men!
~Henry Wadsworth Longfellow
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