What is the difference between hades and hell?
An excellent question, to which I hope I do some justice.
The word "hades" does not appear in the King James Version of the Bible. In the Old Testament the Hebrew word most commonly translated "hell" is sheol, the grave. Thus many people say that the Old Testament had no conception of an afterlife. In the New Testament there are two Greek words that the King James Version often translated as "hell"hades and gehenna. Hades is used eleven times, and gehenna twelve times.
The term "hades" comes from Greek mythology. It was the world of the dead and Hades was the God of the underworld (Pluto was the Roman equivalent). Most of the times the word is used in the New Testament it can be translated as "the grave." (Matt 11:23; Lk 10:15; Acts 2:27, 31 where it is a translation of an Old Testament passage using "sheol") In 1 Cor 15:55 the KJV actually translates it as "grave": "O death, where is thy sting? O grave, where is thy victory?" If this is the common meaning, then that may give a different slant on Matt 16:18, "upon this rock I will build my church; and the gates of hell shall not prevail against it." That would make it read, "the gates of the grave will not prevail." Carrying through with that idea are the four times in Revelation where the word is used (1:18, 6:8, 20:13, 14), where it is always used with the word "death." Hades is cast, with death, into the lake of fire (Rev 20:14), so is not equivalent to the final punishment. There is one other instance of the word that I will cover later.
The term "hell" in the New Testament is generally from the word "gehenna", which is a variation on the Valley of the Sons of Hinnom. This was a valley outside the walls of Jerusalem where, in the years shortly before the Babylonian captivity, some people burned their children to "Molech", the King of the Gods. It later became a city dump, and fires were constantly breaking out there. In the New Testament it is often associated with fire. (Matt 5:22; Matt 18:9; Mk 9: 43, 45, 47; Jas 3:6) It is spoken of as a place of destruction of the body and soul (Matt 5: 29, 30; Matt 10:28; Matt 18:9; Matt 23:15, 33; Mk 9:43, 45, 47; Lk 12:5). Although the word is not specifically used in Revelation, it may be that it could be equated with the lake that burns with fire.
The other instance of the word "hades" is Luke 16:23, in the story of the rich man and Lazarus. Here it is a place of torment, and the only time it is mentioned in connection with fire. It is contrasted with "Abraham's bosom," where Lazarus was taken. It is clearly distinct from the pleasant place of the dead. It is pictured as a place of the dead while there are still others on Earththerefore before the final judgement. Because of this and the passage in Rev 20:14 it has been theorized (only a theory, mind you) that when a man dies he goes either to hades (in anticipation of eternal punishment) or to "Abraham's bosom" (the equivalent of the Muslim idea of Paradise). Then when Christ comes again for the final judgement those who are in "Abraham's bosom" will be judged and taken to heaven, while those in hades will be sentenced to eternal punishment in the lake of fire, which they then call hell. It's a good theory and I accept it, but I would hesitate to be dogmatic about it.
So the essential difference between hades and hell is that hades is generally associated with death and the grave while hell is generally associated with burning and punishment. For all practical purposes in our lives here on Earth there is possibly no real major distinction between the two. They are both characterized as places we don't want to go.