ANSWER: When a person dies, the spirit goes by God’s direction to Hades (one of the words translated as “hell” in the King James Bible), which denotes the “place of disembodied spirits.” This is where Lazarus and the rich man of Luke sixteen went upon their deaths. (This is also where Christ and the “thief on the cross” went when they died. Christ did not ascend to the Father and heaven until forty days after His resurrection - John 20:17 & Acts 1:3. In Acts 2:34, we learn that David is still not ascended into the heavens, because he, too, remains in Hades). Lazarus was carried by angels into the part of Hades referred to as paradise or Abraham’s bosom, while the rich man awoke in the part of Hades referred to as a place of torments! Each of these will remain where they are until the general resurrection of the dead (John 5:28-29). The same is true of David and the “thief on the cross.” In the resurrection, their spirits (and all the dead, righteous and unrighteousness) will leave the Hadean world and rejoin their changed bodies (1 Corinthians 15:51) to stand before Christ in judgment (2 Corinthians 5:10). The righteous (those obedient to Christ) will then go to Heaven (Matthew 25:23). The unrighteous (the disobedient) shall be cast into the lake of eternal fire and brimstone (Matthew 25:41 & Revelation 20:14-15)!

The passages in the question refer to the same place. The word “hell” in 2 Peter 2:4 is from the Greek word “tartarus” and is described as a place of reservation “unto judgment.” The rich man of Luke 16 remains in the same place, i.e., the place of torments, also reserved “unto judgment.” The final destination for the ungodly following judgment is from the Greek word “gehenna,” also translated “hell” in the English (Matthew 10:28).

There is going to be a Judgment Day, because God has appointed it (Acts 17:31) so that: every knee shall bow and every tongue confess (Romans 14:11); everyone shall give account of himself (Romans 14:12); everyone may receive the end result of that which was done in the body (2 Corinthians 5:10); everyone will know exactly the why of their end result (Matthew 25:31-46); and to hear final sentences pronounced (Matthew 25:34; Matthew 25:41).