Hephaestus is the Greek god related to fire and to all the uses we can do of it, including arts and crafts where the burning flame has an essential role. Hephaestus is described as an excellent blacksmith, who realized even the armour, the weapons and the shield of Achilles! It is evident that he is connected with the terrestrial fire, rather than the heavenly fire (the Sun).
The episode when Hephaestus was thrown from the top of Olympus by Zeus (his father, since it is from the Sky that the lightning [an attribute of Zeus] comes, causing, through its contact with trees, the birth of fire) represents the potential inherent of the lightning to bring in itself fire.
The Greeks represented Hephaestus with a blue headgear, to symbolize the Sky from where the fire god comes (via the lightning) and the place where resides the most pure and primordial form of fire, the Sun.
Ptah and Hephaestus:
Anyway the terrestrial fire – came down on the Earth via the lightning or kindled by man – 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 of which we talked before he broke one of his leg), since he can’t walk by himself and needs a wooden support, just like the fire on Earth can’t continue to live without the wood that feeds it.
Prometheus on the other hand is a more complex figure, but still related to fire. He stole some fire from Olympus to donate it to men, meaning that the latter aren’t anymore dependant on Zeus (via the lightning) for their need of fire, they can now obtain it whenever they want. That’s what happens when men learn to kindle a fire.
However, I want to focus on the enchainment and torture of Prometheus: in this case he represents the Sun itself and the myth explains the process of self-combustion through which the Sun feeds of itself and destroying itself stays alive and continues to shine eternally, a sort of unceasing death and rebirth. That’s what happens and 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 while the one on the Sky not, it was self-sustaining and perennial.
Note: a symbolism linked 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 heavenly symbol as well as a solar symbol, so we have more solutions in relation to how we interpret the torture: if we look at the eagle as a solar symbol we have the Sun that devours and sacrifices itself perennially, 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 be fed by the vigor (that was believed to reside in the liver – the part of the body devoured everyday by the eagle -, where vitamin D, the “vitamin of the sun”, resides and accumulates) of the Sun, by the power of its rays.
Only at night Prometheus is exempt from his punishment, as indeed the Sun from its eternal self-sacrifice: at sunset it sinks to the west, in the depths of the underground – the subterranean regions, the realm of death -, to then reappear again in the east the next morning, resurrected. The same journey was accomplished by the spirits of the dead, to then come back again among the living…