What is the difference between Hell and Lake of Fire?

In the commentaries and studies that I'm familiar with, this isn't to be taken as two literally different places,this is merely a literary device. (And this coming from a self-described Biblical literalist.)

For example, from The Pulpit Commentary on the Bible Hub page:

(2) The sea being a type of the ungodly nations, the sentence may mean those spiritually dead, but living on the earth at the time of the judgment. The next clause seems to support this view. And death and hell delivered up the dead which were in them; death and Hades (see Revelation 1:18; Revelation 6:8). As in Revelation 6:8, the two - really one - are mentioned separately, the latter being looked upon as the guard house of those whom the former has seized. This clause, taken in conjunction with the preceding one, may mean - From the ungodly nations, those physically living but spiritually dead were called up for judgment, and also those who were actually dead, having been seized by death and Hades.

Also, from Jamieson-Fausset-Brown Bible Commentary

1. death and hell—Greek, "Hades." The essential identity of the dying and risen body is hereby shown; for the sea and grave give up their dead. The body that sinned or served God shall, in righteous retribution, be the body also that shall suffer or be rewarded. The "sea" may have a symbolical [Cluver from Augustine], besides the literal meaning, as, in Re 8:8; 12:12; 13:1; 18:17, 19; so "death" and "hell" are personifications (compare Re 21:1). But the literal sense need hardly be departed from: all the different regions wherein the bodies and souls of men had been, gave them up.

Matthew McGee has a fairly comprehensive teaching on Hell that would seem toagree.

The English word "Hell" refers to a place of eternal punishment for the wicked. Its meaning does not distinguish between the two separate places for the wicked to be punished, one temporary for the soul, and the other, the Lake of Fire, permanent for the soul and body. Nor does its meaning include the place of comfort for saints prior to Christ's resurrection. In normal English conversation, "Hell" is used only in the negative sense, with no saved people ever going there.

I have spent many hours researching that particular question, but do not have a definitive answer for you. I will give you some of the Scriptures which may or may not clear this up for you.

I am not sure but I have come to these possible conclusions:

Hell and the bottomless pit may indeed be the same place.

Eze 31:2, 3,16, and 17 KJV

2 Son of man, speak unto Pharaoh king of Egypt, and to his multitude; Whom art thou like in thy greatness?

3 Behold, the Assyrian was a cedar in Lebanon with fair branches, and with a shadowing shroud, and of an high stature; and his top was among the thick boughs.

16 I made the nations to shake at the sound of his fall, when I cast him down to hell with them that descend into the pit: and all the trees of Eden, the choice and best of Lebanon, all that drink water, shall be comforted in the nether parts of the earth.

17 They also went down into hell with him unto them that be slain with the sword; and they that were his arm, that dwelt under his shadow in the midst of the heathen.

I am intrigued by the part that says:

I made the nations to shake at the sound of his fall, when I cast him down to hell with them that descend into the pit:

There is also a Proverb which causes me to believe that they may be the same, but different from the grave.

Proverbs 1:12 KJV

Let us swallow them up alive as the grave; and whole, as those that go down into the pit:

and the following Psalm seems to indicate that Hell is separate from the grave.

Psalms 30:3 KJV

O Lord, thou hast brought up my soul from the grave: thou hast kept me alive, that I should not go down to the pit.

As far as the lake of fire Jesus said that it was prepared as a place of eternal punishment for the Devil and the fallen angels

Mat 25:41 KJV

Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:

Revelation tells us that it will also be the place for eternal punishment for the unsaved.

Revelation 14:9 through 11 KJV

9 And the third angel followed them, saying with a loud voice, If any man worship the beast and his image, and receive his mark in his forehead, or in his hand,

10 The same shall drink of the wine of the wrath of God, which is poured out without mixture into the cup of his indignation; and he shall be tormented with fire and brimstone in the presence of the holy angels, and in the presence of the Lamb:

11 And the smoke of their torment ascendeth up for ever and ever: and they have no rest day nor night, who worship the beast and his image, and whosoever receiveth the mark of his name.

and I have concluded most possibly Hell and the bottomless pit may indeed be one and the same; and is a temporary holding place for at least some of the fallen angels, as well as those who reject salvation, to await the great white throne judgment.

I have also concluded that the grave is a temporary holding place for Christians to await the judgment of the righteous, but I still have not been able to reconcile that with Jesus telling the thief on the cross that today he would be with Jesus in Paradise. I do have a possible solution for that , but will keep that to myself since I have not researched it completely.