Minya is the original Son of Godzilla; the very first child the big guy has had. While little is known about Minya's biological connection to Godzilla, I should think that they're directly related; Minya still has the atom breath but seems to have been adopted by Godzilla rather than being a direct son. Godzilla came upon the egg on Sollgell Island being attacked by a horde of Kamakiras and quickly kicked ALL their butts. He then adopted the creature that hatched, Minya. This leads one to believe that Minya isn't Godzilla's naturally born child. Still, he can blow atom breath so he may be of a similar race. I personally like Minya best.
Little Godzilla is the older form of Baby Godzilla. After playing near the tear gas mines, he was viciously attacked by the conniving Space Godzilla on Birth Island, and Little Godzilla showed marks of valor when he desperately attempted to fight back. However, Space Godzilla was too powerful for both he and his father and so he was imprisoned in a crystal cage.
When Godzilla defeated Space Godzilla, Little Godzilla was freed. He is sometimes called "Chibi Gojira" for his admittedly.. umh.. cutesy appearance. I am rather fond of Little Godzilla but it seems that he's not been quite so well received in some scattered areas. His powers are pretty much limited to being able to belch radioactive bubbles and moan piteously, but he struck us as a lovable character in the tapestry of Godzilla-dom.
Godzilla
Junior is the mutated form of Little Godzilla. In the natural radioactivity
and uranium deposits that occurred on Birth Island that ended up giving
Godzilla a nuclear reaction and eventually triggering his meltdown, Little
Godzilla was quickly mutated into a newer, bigger form with a full atomic
breath developed. In the process the island was also reduced to nothingness
and the two were separated. Godzilla Junior quickly appeared off the coast
of Japan and was used much to the disgust of Miki Saegusa as a way to get
Godzilla to come to Tokyo. In a heated battle with the aggregate Destroyer,
Junior first used his powers to their limit and dispatched of the creature
after much difficulty using his admittedly smaller and less powerful heat
ray.
Junior
and his father then regrouped (see right image above), but their reunion
was short lasted because it was then that the adult Destroyah attacked.
He quickly made short work of Junior by strangling him, flying off with
him in that admittedly uncompromising position and finally smashing him
onto the ground. Godzilla tried to breath life back into his son but was
unsuccessful in his attempts. In a fit of mad rage he quickly attacked
Destroyer and then melted down.