The concept of Hades is developed in the New Testament. Jewish scholars of the LXX translated the Hebrew term "sheol (šᵉ'ôl)" using the Greek term "hadēs." They understood that this was the underworld that received all of the dead.

The Hebrew term "sheol," in all its uses in the Old Testament, appears to be a place where all dead people to to, whether non-Believer or not. Furthermore, sheol appears to be a metaphorical way of describing a grave more so than describing a shadowy region of the netherworld or a temporary place the dead go to before judgment.

Hades: In contrast to LXX's use of the hadēs (Greek) to translate the sheol (Hebrew), Jesus use of hadēs" indicates a distinctly different meaning from the Hebrew concept of sheol.

Hades is a contrast to heaven as a place for souls. Yet, there is a suggestion of being located within earth not unlike sheol.

And you, Capernaum, will you be exalted to heaven? You will be brought down to Hades! (Luke 10:15; Matt 11:23)

And I also say to you that you are Peter, and upon this rock I will build My church; and the gates of Hades will not overpower it. (Matt 16:18)

Hades is the destination for the souls of non-Believers.

And in Hades he lifted up his eyes, being in torment, and saw Abraham far away and Lazarus in his bosom. (Luke 16:23)

Because You will not forsake my soul to Hades, Nor give Your Holy One over to see corruption. (Acts 2:27)

he looked ahead and spoke of the resurrection of the Christ, that He was neither forsaken to Hades, nor did His flesh see corruption. (Acts 2:31)

Then I looked, and behold, a pale horse; and he who sits on it had the name Death, and Hades was following with him. Authority was given to them over a fourth of the earth, to kill with sword and with famine and with pestilence and by the wild beasts of the earth. (Rev 6:8)

Hades is the temporary location for the souls of non-Believers before Judgment.

and the living One; and I was dead, and behold, I am alive forever and ever, and I have the keys of death and of Hades. (Rev 1:18)

And the sea gave up the dead which were in it, and death and Hades gave up the dead which were in them, and they were judged, every one of them according to their deeds. Then death and Hades were thrown into the lake of fire. This is the second death, the lake of fire. (Rev 20:13-14)

Hell: The English term "hell" is translated from the Greek term "gehenna." Gehenna does not appear in the LXX or extrabiblical Greek literature; it is a word formed from the use of the Latin alphabet used to transliterate the Hebrew name Hinnom. The Valley of Hinnom, south of Jerusalem, was where Jerusalem's garbage and dead animals were cast out and burned. Around the hills of the valley, Israelites sacrificed children in the worship of Baal, which garnered God's judgment (Jer 7:30-31; 19:2-7). The image of the valley's constant burning of undesirable waste, stench, smoke and God's judgment developed to symbolize as the place of punishment and final judgment. Even though it no longer referred to the valley itself, it ultimately became a metaphor for the place of eschatological fire in hell.

Hell is a place for non-Believers.

"Woe to you, scribes and Pharisees, hypocrites, because you travel around on sea and land to make one proselyte; and when he becomes one, you make him twice as much a son of hell as yourselves. (Matt 23:15)

Hell is a destination after a judicial process.

You serpents, you brood of vipers, how will you escape the sentence of hell? (Matt 23:33)

Hell is a place of unquenchable fire that a non-Believer is thrown or cast into.

And if your hand causes you to sin, cut it off; it is better for you to enter life maimed, than, having your two hands, to go into hell, into the unquenchable fire. And if your foot is causing you to sin, cut it off; it is better for you to enter life without a foot, than, having your two feet, to be thrown into hell. And if your eye is causing you to sin, throw it away; it is better for you to enter the kingdom of God with one eye, than, having two eyes, to be thrown into hell, (Mark 9:43-47)

But I will show you whom to fear: fear the One who, after He has killed, has authority to cast into hell; yes, I tell you, fear Him! (Luke 12:5)

And the tongue is a fire, the very world of unrighteousness; the tongue is set among our members as that which defiles the entire body, and sets on fire the course of our existence, and is set on fire by hell. (Jas 3:6)

Lake of Fire: The Lake of Fire is only mentioned in the last book of the Bible – Revelation. Unlike Hades which is where the souls of non-Believers reside after death, the Lake of Fire is introduced after all of the dead are resurrected. Hell and the Lake of Fire appear to be synonymous where hell is a simpler conceptual term without requiring any understanding of the details of resurrection and the Great White Throne of Judgment.

The Lake of Fire, like Hell, is an eternal place that resurrected non-Believers and evil beings are tossed or cast into.

And the beast was seized, and with him the false prophet who did the signs in his presence, by which he deceived those who had received the mark of the beast and those who worshiped his image. These two were thrown alive into the lake of fire which burns with brimstone. (Rev 19:20)

And the devil who deceived them was thrown into the lake of fire and brimstone, where the beast and the false prophet are also, and they will be tormented day and night forever and ever. (Rev 20:10)

But for the cowardly and unbelieving and abominable and murderers and sexually immoral persons and sorcerers and idolaters and all liars, their part will be in the lake that burns with fire and brimstone, which is the second death." (Rev 21:8)

The Lake of Fire will be the location for all things that God deems evil.

Then death and Hades were thrown into the lake of fire. This is the second death, the lake of fire. And if anyone's name was not found written in the book of life, he was thrown into the lake of fire. (Rev 20:14-15)

Miscellaneous distinction: The abyss is a place within earth that imprisons fallen angels (Luke 8:31; Rev 9:1-11).