Yes, the Bible calls God’s final judgment of the wicked an ‘everlasting fire’ or by most translations an ‘eternal fire”. I think either English word translated from the Greek word there is fine for our purposes. I’m not sure (though I have a suspicion) why the KJV and NKJV translate the same word once as everlasting and once as eternal, but either way is fine by me. Annihilationism does recognize the wicked’s final judgment/punishment is just as everlasting/eternal as the saved’s eternal life is going to be.
However, what the annihilationist also recognizes is that God’s eternal/everlasting fire is also (and not to be overlooked) a consuming fire. One that burns up the wicked. AND (most importantly), we don’t just come up with this idea out of thin air. It’s Scripturally taught (in my opinion) via the following passages: (please note that any/all ECT poster is welcome to address any of these passages listed below as I wouldn’t want to be taking any out of context toward the final fate of the wicked.). My confusion is, I don’t think God intended for us to assume His eternal fire is not also a consuming fire.
'Eternal' connotes a sense of timelessness; no beginning and no end. For instance God's word is eternal. It goes on forever. It doesn't pass away. So consider what Jesus said. Speaking of the punishment, Jesus said, 'there they will weep and gnash their teeth'. So there is a place where they will weep and gnash their teeth. Annihilation denies the truth of this statement. Once they are annihilated, their punishment would end. They would no longer be in a place of torment. Their weeping and gnashing of teeth would cease. Moreover it suggests there will be a time when the word of God is not true anymore; they won't be weeping and gnashing their teeth. And Jesus' statement that they will weep and gnash their teeth will become untrue.
The godless who don't believe in anything after death would love this to be true. If at some time they were annihilated, so what? But Jesus clarifies our understanding when he says they will be thrown into hell 'where their worm does not die and the fire is not quenched'. Mark 9: 47,48