Abyssos has been translated as “the deep” in the KJV, or “the abyss” in other translations
“And Jesus asked him, saying, What is thy name? And he said, Legion: because many devils were entered into him. And they besought him that he would not command them to go out into the deep [abyssos]” (Luke 8:30-1).
“But the righteousness which is of faith speaketh on this wise, Say not in thine heart, Who shall ascend into heaven? (that is, to bring Christ down from above:) Or, Who shall descend into the deep [abyssos]? (that is, to bring up Christ again from the dead.)” (Romans 10:6-7).
Alma 30:11-4 states that spirits will be in a state of paradise or outer darkness. So since Christ descended into the abyss as a spirit, the abyss has some association with outer darkness.
Abyssos has also been translated as “the bottomless” in the KJV
“And the fifth angel sounded, and I saw a star fall from heaven unto the earth: and to him was given the key of the bottomless [abyssos] pit [phrear]. And he opened the bottomless [abyssos] pit [phrear]; and there arose a smoke out of the pit, as the smoke of a great furnace; and the sun and the air were darkened by reason of the smoke of the pit” (Revelation 9:1-2). So in other translations, abyssos phrear is translated as “the pit of the abyss.”
Abyssos has also been translated as “the bottomless pit” in the KJV
“And they had a king over them, which is the angel of the bottomless pit [abyssos]” (Revelation 9:11).
“And when they shall have finished their testimony, the beast that ascendeth out of the bottomless pit [abyssos] shall make war against them, and shall overcome them, and kill them” (Revelation 11:7).
“The beast that thou sawest was, and is not; and shall ascend out of the bottomless pit [abyssos], and go into perdition [apōleia]” (Revelation 17:8).
Therefore, being in the abyss is not exactly the same as being in perdition/destruction.
“I saw an angel come down from heaven, having the key of the bottomless pit [abyssos] and a great chain in his hand. And he laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him a thousand years, And cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more, till the thousand years should be fulfilled” (Revelation 20:1-3).