>>104538420>>104538706Normie-tier explanation. The Rival was never "the Reverse-Flash", Jay Garrick just compared him to RF in the Nineties.
Eobard Thawne was named Zoom, Professor Zoom and Reverse-Flash all in his very first appearance. His main title has always been Zoom (because it's a bother to spell "Professor Zoom" all the time), while "Reverse-Flash" is more of a moniker, like Batman is "the Dark Knight" and "the Caped Crusader". Lately in Rebirth, however, DC has been catering to the the normiefag show audience and trying to low-key refer to "Reverse-Flash" as his main title full time (in comparison, the New52 version was never called RF at all, only Zoom).
Hunter Zolomon is the second Zoom, and the second Reverse-Flash. He ALSO refers to himself by both titles as soon as his second issue after getting powers. He wasn't called "Professor Zoom", because he was an ex-FBI and a cop, not a Professor (although in SIlver Age Eobard also wasn't a real professor, but rather a super-smart thief, who got the nickname "Professor" in the criminal world - but that got retconned at the very least by the time of his joining of Wizard's Secret Society)
New52 also had Wallace West's father Daniel as "the Reverse-Flash", who's never been called Zoom.
That's it. There's been no other Reverse-Flash. Rival and Inertia have been compared to them ("you could say he is my Reverse-Flash"), and Savitar had some elements hinting at him being an RF candidate (his mask) before being dropped. So, there is not really "a difference": there's the first Zoom/RF, and the second one.