Everything you know is wrong--Godzilla only officially appeared in one movie (Godzilla, King of the Monsters (1954)). Other than that (plus remakes like Godzilla 1985 and the stupid American version starring Ferris Buehler) Godzilla never appeared in another movie.
Godzilla never fought Mothra, Rodan, King Kong, Mechagodzilla, Ghidrah, Angilas, Spigas, the Smog Monster or anyone else.
In all those cases, the monster called Godzilla was really Gigantis.
Gigantis, the Fire Monster (1959) was sort of a sequel to Godzilla, with two mutant prehistoric monsters--Gigantis and Angilas-- awakened from the sea and brought havoc to modern Japan. At the end of the movie, Gigantis was buried in an avalanche and left under a mountain of ice. A few years later, he broke free and suddenly everyone called him Godzilla.
Gigantis came out a few years after the original Godzilla movie and bombed in both Japan and America. The monster was still a guy in a rubber suit that looked exactly like Godzilla except for slight modifications with the teeth and ears.
Toho Productions decided to go with name recognition so when the monster got loose again in 1962, it was King Kong vs. Godzilla. There's never been an official explanation--continuity doesn't matter a whole lot in giant monster movies.
It's not that Gigantis is known for his conversation so it doesn't really matter but the real Godzilla died at the end of his first movie (which most people have never seen) and most of his fame comes from an entirely different monster.