D&C 19 clarifies the term “eternal” as the word has been translated in the scriptures. In English “eternal” means “without ending or beginning”, but in Hebrew, the word is “olam”, and in Greek, the word is “eonian”. Those words mean an age, a period of time, a world, a condition of existence, an estate. And in all these cases, there is definitely a beginning and an end.
Alma was “racked with eternal torment”, but after he repented, he “could remember [his] sins no more. So, “eternal” doesn’t mean what we commonly think it means.
Alma 36:12 But I was racked with eternal torment, for my soul was harrowed up to the greatest degree and racked with all my sins.
Alma 36:13 Yea, I did remember all my sins and iniquities, for which I was tormented with the pains of hell; yea, I saw that I had rebelled against my God, and that I had not kept his holy commandments.
Alma 36:14 Yea, and I had murdered many of his children, or rather led them away unto destruction; yea, and in fine so great had been my iniquities, that the very thought of coming into the presence of my God did rack my soul with inexpressible horror.
Alma 36:15 Oh, thought I, that I could be banished and become extinct both soul and body, that I might not be brought to stand in the presence of my God, to be judged of my deeds.
Alma 36:16 And now, for three days and for three nights was I racked, even with the pains of a damned soul.
Alma 36:17 And it came to pass that as I was thus racked with torment, while I was harrowed up by the memory of my many sins, behold, I remembered also to have heard my father prophesy unto the people concerning the coming of one Jesus Christ, a Son of God, to atone for the sins of the world.
Alma 36:18 Now, as my mind caught hold upon this thought, I cried within my heart: O Jesus, thou Son of God, have mercy on me, who am in the gall of bitterness, and am encircled about by the everlasting chains of death.
Alma 36:19 And now, behold, when I thought this, I could remember my pains no more; yea, I was harrowed up by the memory of my sins no more.
I don’t know what Joseph Smith was thinking. He probably had trouble comprehending what the Lord was trying to reveal, but he was really trying to undo centuries of false traditions due to mistranslations of the Bible. Just because you receive revelation doesn’t necessarily you understand what you receive or can easily put it in words. This was probably new to him also.
“Eternal punishment is God’s punishment”, means it’s the kind of punishment ordained by God. And, by the same token “Eternal life is God’s life”, or the kind of life that God lives. We say “eternal life is to know God”, but nobody can truly know God unless he IS God. Then, and only then can you live as God lives.
This is Bruce R. McConkie from A New Witness for the Articles of Faith, page 492:
There is a true doctrine on these points, a doctrine unknown by many and unbelieved by more, a doctrine that is spelled out as specifically and extensively in the revealed word as are any of the other revealed truths. There is no need for uncertainty or misunderstanding. And surely if the Lord reveals a doctrine, we should seek to learn its principles and strive to apply them in our lives. This doctrine is that mortal man, while in the flesh, has it in his power to see the Lord, to stand in His presence, to feel the nail marks in His hands and feet, and to receive from Him such blessings as are reserved for only those who keep all His commandments and who are qualified for that eternal life, which includes being in His presence forever. [Forever means now and always.]