There has been a lot of discussion lately regarding how the different Godzilla movies relate to each other, and events in certain movies have been used to help "prove" various theories about Godzilla. For example, the treatment of the title monster in "Gigantis, The Fire Monster" as a separate monster than the one in "Godzilla, King of the Monsters" has led some people to argue that the Godzilla portrayed in all the movies after the first one was, in fact Godzilla's mate, and is therefore female.
So, what's the truth? Beats me! What's my opinion on the subject? Read on ...
Essentially, the early Godzilla movies weren't attempting to achieve any sort of coherent continuity among the various films. The first movie was meant as a one-shot "movie with a moral", and Toho was as surprised as anyone when the movie did well enough to warrant a sequel. Although the second movie, "Gigantis, The Fire Monster", did make reference to the first movie, it claimed that both monsters were members of a species of "fire monsters" which had been around since prehistoric times, whereas the first movie indicated that Godzilla was created through man's testing of atomic weapons.
In the next movie, "King Kong vs. Godzilla", Godzilla was treated as if no one had ever seen him before. Instead, he was believed to be a "prehistoric species of dinosaur" who had been lying dormant, frozen in an iceberg, for almost 100 million years.
I've always liked to think of there being only one Godzilla for all the original movies, with the thought that somehow he regenerated from his "death" in the first movie. Basically, if there were more than one of him around, why would only one show up at a time? Why would they take turns attacking Tokyo? Having said that, though, he did disintegrate pretty thoroughly at the end of the first movie, so maybe this is just wishful thinking on my part.
With the release of "Godzilla 1984" (a.k.a. "Godzilla 1985"), Toho made a conscious decision to rewrite Godzilla history. All the movies after the original were deemed to have never happened at all. Thus, any discussion of the later Godzilla being the original Godzilla's mate appear to be mooted.
For a while, the new series attempted to follow a strict continuity, with each movie picking up where the previous one left off, and with frequent references being made to previous films. Thus, at the end of "Godzilla 1984", Godzilla falls into a volcano, and in "Godzilla vs. Biollante", Godzilla arises from the same volcano. Similarly, in "Godzilla vs. Biollante" Biollante heads off into space, and in "Godzilla vs. Space Godzilla" there is speculation that Space Godzilla could have been created from some of Biollante's cells carried into space. In "Godzilla vs. Mechagodzilla", it is revealed that Mechagodzilla was built using technology gleaned from the cybernetic version of King Ghidorah from "Godzilla vs. King Ghidorah". Finally, "Godzilla vs, Destroyer" comes full circle and has a monster created from the device which originally defeated Godzilla in the first Godzilla movie.
All of this carefully maintained continuity, however, falls apart with the events depicted in "Godzilla vs. King Ghidorah". In that film, time-travelers remove Godzilla from the island where he was exposed to the nuclear bomb test which turned him into everyone's favorite radioactive reptile in the first place. Unfortunately for the time-travelers, Godzilla lies dormant in the ocean near Tokyo until he is exposed, many years later, to the radiation given off by a sunken nuclear submarine. This means that, not only did the original "Godzilla, King of the Monsters" never take place, but neither did the events portrayed in "Godzilla 1985" or "Godzilla vs. Biollante"! And if these movies never occurred, then where did Space Godzilla and Destroyer come from?
Anyway, the point is that the movies that make up the so-called "Heisei" series [from "Godzilla 1984" through "Godzilla vs. Destroyer"] did follow a loose continuity that was unfortunately mucked up royally by the time-travel events in "Godzilla vs. King Ghiodrah."
[And then, of course, you have the so-called "American Godzilla" movie, which has nothing whatsoever to do with any of the other Godzilla movies and isn't really a Godzilla movie in the first place, so I'm not sure why I even bother mentioning it....]