Rufous

As the author of Rufus, I can tell you exactly what happened.

First of all, Rufus didn't damage your USB drive. It only removed the letter Windows assigned it, which it needs to do to be able to repartition and format it, and since you cancelled that operation, the drive letter was not assigned back. This is why you couldn't see it in Explorer, but you could still see it in Device Manager/Disk Manager.

The simple option, to make your drive listed again so that you could format it and get a letter reassigned, was to follow this entry from the Rufus FAQ. A couple of clicks in Rufus was all that was needed.

Also, the latest versions of Rufus has improved the default enumeration process and will automatically list raw or unpartitioned drives, so you should no longer have to do anything even if you cancel in the middle of a bad blocks check or a format operation.