And the answer is: NADA!
At least as far as we can see.
For the particular person, a gem could be a stone left in its natural state while a jewel is more refined and ornamental.
Thus if this is a gem:
Then this is a jewel:
And someone we have listened to once or twice:
So, show us your jewels and gems, if you wish. Send your images to firstname.lastname@example.org by 2PM Tuesday, September 6, 2016 along with whatever message you want to add and your blog post, if applicable. We'll post them later the same day.
Have a brilliant day!