The words they use are almost identical, but in context those words mean different though related things. As 1 John 4:17 makes clear, John is speaking of those who fear the punishment that will attend the Second Coming. The torment or punishment of which verse 18 speaks is the torment of God's judgment. John says that if we have perfect love, we have no need to fear that judgment.
Scripture also teaches that there is no punishment, no exclusion from the kingdom, for those who come to Christ (John 6:37; see also D&C 84:37-38). It follows that those who anticipate God's punishment—exclusion from his kingdom—are already punished. They—we?—are already excluded, already punished, if they fear divine judgment. It isn't that God excludes and punishes us, but that we exclude and punish ourselves, and our fear is a mark of that exclusion. The Father invites us to enter into his kingdom through his Son. Those who sin and refuse to come to the Son refuse to enter. Their refusal is their punishment.
We sometimes hear it said that Christians live their lives in fear of what God will do to them if they do not obey him. That's a common theme in many contemporary criticisms of religion in general and Christianity in particular. I don't deny that I've known people who understand Christianity in those terms. But 1 John 4:17-18 teaches that if we do live in fear of a coming divine punishment, then we are not yet Christians. Perfect love, the love of God (meaning here the love that imitates his love), would cast out all such fear.
How do we have that perfect—in other words, "full grown," "mature," "fully developed"*—love? Not surprisingly, John says we have it by loving one another: if we love one another, then even in this world we are as God is, because his love is in us: "If we love one another, God dwells in us" (1 John 4:12). And his indwelling love is perfected, reaches the zenith of its perfection, in our love of one another. John does not say so, but it takes little to conclude that we see the perfected love of God in the self-sacrifice of his Son, which says everything about what it means for God's love to be perfected in the church.
It is probably not surprising that a Christian text would suggest that love for one another in the community of believers and, by extension, love for those who are not in that community make us like God. But there is a surprise for us if we are too impressed with the Christian's special status with God. If his love is perfected in those who love one another as he loves, then it is also perfected in those who are not Mormon, nor otherwise Christian, but who love one another selflessly. Implicate in 1 John 4:12 is the claim that the love of Islamic charity or Confucian magnanimity or Sikh service to humanity also incarnates God's perfected love. Given what we see in the news and given what I sometimes hear at church, that would be surprising to some Christians. Less surprising, however, is what I take John also to mean: God cannot be in us, in our community, if we do not love fully.
John's message is about love in the community. Of course it has implications for the individuals in the community. There is no communal love without loving individuals. But John's theme is the love found amongst us as a body more than it is the love that a particular person ought to have.
In contrast, Mormon's message is about the love of an individual. He writes a letter about the baptism of children and in an aside says that he is not afraid of what men can do to him because a person filled with charity, God's everlasting love (verse 17), does not fear. Why? Because "perfect love casteth out all fear" (Moroni 8:16).