Since we've talked about the 2014 Godzilla movie, we might as well talk about the 1998 one too—and share the fact that Toho hated it so much, they changed the canon of the franchise to erase it from existence.
As bad as the reaction to the 1998 film was in the west, in Japan it was so, so much worse. One of the actors who actually played Godzilla, Kenpachiro Satsuma, went so far as to walk out of an early screening, angrily telling everyone present "it's not Godzilla, it doesn't have his spirit." Along with its unappealing design, many Japanese critics pointed out that it didn't make sense that a creature birthed by a nuclear explosion seemed afraid of missiles shot from helicopters.
When rights to the franchise reverted back to Toho after TriStar wisely chose not to try making a sequel to the 1998 movie, the company started a systematic campaign to wipe it out of official Godzilla history. The company started by dubbing the creature "Zilla" as a nod to TriStar taking "the god out of Godzilla," then put it into the film Godzilla: Final Wars, where it was unceremoniously clubbed to death by the real Godzilla.
Along with being used to establish that Zilla and Godzilla are two distinct entities, the film also shows that Zilla is significantly weaker by having his only fight scene against Godzilla end in less than 10 seconds. As a further insult, Zilla is rendered using intentionally crappy CGI and generic American rock music plays in the background as Godzilla pulverizes it into goo with his fire breath.
Toho has since featured Zilla in several comics, in which characters often note how it's usually mistaken for the real Godzilla—but is nowhere near as cool or strong—seemingly just to rub it in.