Hephaestus is the Greek god related to fire and all the uses we can do of it, and he is described as an excellent blacksmith, who realized even the armour, weapons and shield of Achilles: he is clearly related with terrestrial fire, rather than with heavenly fire, i.e. the Sun. The episode when Hephaestus is thrown from the top of Olympus by Zeus symbolizes the potential inherent in lightning to bring in itself fire, since it is from the Sky that the lightning – an attribute of Zeus – comes, causing, through its contact with trees, the birth of fire.
The Greeks represented him with a blue headgear to symbolize the Sky, the place from where he comes via the lightning and where resides the Sun, the most pure and primordial form of fire.
Ptah and Hephaestus:
Anyway the terrestrial fire is less intense than that of the Sun and needs to be rekindled and sustained, or it will fade; that’s why one of the epithets of Hephaestus is “the lame” (after the fall mentioned above he broke a leg), since he can’t stand on his legs and needs a wooden support, just like the terrestrial fire that can’t continue to live without the sustain of the wood that feeds it.
On the other hand Prometheus stole some fire from Olympus to give it to men, in the sense that he teached them how to light a fire so that they didn’t depend anymore on Zeus, via the lightning, to obtain it and benefit from it .
I want instead to focus on the enchainment and torture of Prometheus: in this case he represents the Sun itself and the myth reveals the process of self-combustion through which the Sun, in a sort of unceasing death and rebirth, feeds of itself to keep burining and shine eternally; our ancestors maybe didn’t knew this process of self-combustion of the Sun but they noticed that the terrestrial fire needed to be rekindled and sustained whereas the one in the Sky not, it was self-sufficient and perennial.
Note: a symbol related to the same process can be found in the figure of the Phoenix, known as Bennu among the Egyptians, the eternal bird able to be reborn from its own ashes.
Prometheus is tortured by an eagle, a solar symbol as well as a heavenly symbol, so we have more solutions to interpret the torture: if we look at the eagle as a solar symbol we have the Sun that devours and sacrifices itself unceasingly, coming back to life every day and therefore continuing to shine; if we look at the eagle as a heavenly symbol then we have the Sky nourished by the liver of Prometheus, because the Sky to keep on shining must feed on the vigor (that was believed to reside, as well as the fundamental Vitamin D that the Sun gives us, in the liver, the part of the body devoured everyday by the eagle) of the Sun, i.e. on the energy of its rays.
Only at night Prometheus is exempt from his torture, as indeed the Sun from its eternal self-sacrifice; at sunset it sinks in the west, in the depths of the underground, the realm of death, to then reappear again in the east the next morning, resurrected: thanks to its guide the same journey was accomplished by the spirits of the dead, so as to be able to come back to life again.