Hell from Christianity and in the Book of Revelation is described as a lake of fire where sinners will be cast into and suffer for all eternity with no hope of escape since they are already dead. Other depictions of Hell describe it as a place of solitude and darkness. Either way, it is a place of eternal pain with no hope of escape.
In Revelation 20:14, Hell is thrown into the lake of fire, showing that they're not the same thing.
Greek mythology is full of these since many things were immortal. Prometheus was condemned to this by Zeus for stealing fire. He was chained to a rock where an eagle would eat his liver each day. As a Titan god he could not die and his liver would always grow back. In some versions an adamantine spike was driven through his chest for good measure. His harsh punishment is sometimes stated to also be because he refused to tell Zeus who was destined to over throw him so Zeus would never release him. He got off lucky thanks to Hercules freeing him thousands of years later since Prometheus had information Hercules needed.
Sisyphus was forever forced to roll a boulder up a mountain, just to watch it roll back down every time he reached the top.
The Titans themselves were condemned to an eternity in Tartarus, a dark pit for their war against Zeus.
Atlas had to hold up the heavens forever.
The sky god Uranus was castrated by his son Kronos and must spend all time unmanned.
The centuar Chiron was poisoned by hydra blood and could not heal himself, but due to being the son of Kronos he was immortal which would have left him in agony. Once again Hercules saved the day by arranging from him to die.
Typhon. Trapped forever under Mount Aetna.
Loki from Norse Mythology was chained to a rock by the entrails of his own children with a snake dripping poison over him till the end of time for the murder of Balder among other acts. His wife only provide a brief respite from the pain by collecting the poison in a bowl that must be periodically dumped. Decrees of fate prevent him from dying or being freed. The only time he will be freed is to die in the final battle that ends the world.