Also, summons in FFVII now have a clear explanation!
The summoned beasts are thematically and in lore, like the Eidolons of FFIX. They are creatures born from spirit energy, based on the legends and mythologies of numerous peoples that have existed since the beginning of time on the Planet. These conjoined memories of said legends, mythologies and folklore enter the collective spirit energy as part of the peoples' heritage, and manifest into these magical creatures, which the planet then creates or manifests via materia.
Ifrit is a god of fire thought to have given man the gift of flame.
Shiva is the manifestation of a queen who healed the planet's physical wounds with ice, which can still be seen in the permafrost of the polar lands.
Leviathan is unsurprisingly, a deity that was worshiped to protect the lands from floods. Most adherents of this belief system live in..Wutai.
Fat Chocobo is manifestation of a legendary chocobo which became a symbol of fertility and good fortune. It commonly appears in fairy tales.
Bahamut is a dragon deity worshiped by the earliest of the planet's civilizations. And it is believed there are many different versions, each with its own powers and unique appearances.
FFVII and FFIX share almost the exact same planetary lore and cosmology. Nevermind FFX, the world of FFVII and Gaia are like... The same now.