How Do SSDs Wear Out?

I understand that HDDs can have mechanical failures, but when SSDs came on 
the scene, I wondered how it is that SSDs 'wear' out.  I've got many 
machines with HDDs (one is a 20 year old XP box, still working fine) and 
some with SSDs, none of which have failed.  I've also got many external 
HDDs, all still good.

Anyway, I've always heard that SSDs can wear out after many writes.  I 
started to read about the physical construction of  SSDs, but I ended going 
down the rabbit hole, reading about wear leveling and, of course trim, but 
never found anything about *why* a SSD 'wears' out.

How does a SSD wear out?  And while I'm asking, does the same 'wearing' out 
occur happen on a USB flash drive?

Thanks.