Eternal punishment for some translates as death ever after, the second death, as Scripture promises is the wages of sin/disobedience to God starting in Genesis. Others equate eternal punishment with torture and torment, thinking the person must be conscious for punishment to be effective, which is obviously defective thinking, since even in our justice system, death is seen as very much the most harshest punishment possible.
"Then they will go away to eternal punishment, but the righteous to eternal life."
In the verse above, we have the same word (Aionios) describing the eternal state of both the righteous and the unrighteous. That being said, the meaning must be the same for both. We know that eternal life for believers refers to unending life. Likewise, Eternal punishment must also mean unending punishment.
The Greek word is from the primary ollumi ἀπόλλυμι (to destroy utterly, kill,
slay; to perish; abolish etc); ruination, i.e. Death, punishment -- destruction.
Of course I agree the word means the same thing: eternal. However that in no way translates to eternal torture or torment. I am not sure how or why anyone thinks it does, quite honestly. Once a person is dead from the second death in the lake of fire, it is eternal ever after. There is no coming back from it. That does not make it eternal torture though. There is a plethora of Scripture to support my view of death and destruction (I gave some of them already) being the wages of sin. The Bible states that death is the penalty for sin right from the early stages of Genesis. How it can be overlooked and have God turned into a sadistic monster to torture and torment the creation He gave the life of His only begotten Son for, instead, I may never understand aside from saying that people have been deceived by the lies of Satan.
Eternal life is given (extended to us) only through accepting the
propitiatory sacrifice made by Jesus Christ on our behalf.