Apart from the obvious difference that 'jewel' can be used metaphorically, 'jewel' is an all-embracing term for both precious stones (rubies, diamonds and the like) and 'semi-precious stones' (agates, opals and the like); and perhaps also for something that's not a stone at all (like a pearl).
PS I say 'perhaps' because I'm just not sure. I'm sure some web-page out there will explain aNY differences there may be. For example, there is something called 'costume jewellery' which uses materials that probably wouldn't be called 'jewels' at all.
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