I wouldn't want to push the similarities too far, but Mormons understand one of the principle aims of religion—salvation—as do those in the Eastern Orthodox and Wesleyan traditions. For many believers, salvation means the removal of sin, atonement. But for Orthodox, Wesleyan, and Mormon Christians it means partaking in the divine nature:
By his divine power the Lord has given us everything we need for life and godliness through the knowledge of the one who called us by his own honor and glory. Through his honor and glory he has given us his precious and wonderful promises, that you may share the divine nature. (2 Pet. 1:3-4; Common English Bible translation)
We differ about the divine nature. We differ about what it means to partake in that nature. (Mormon theology may not be conceptually clear about what we mean by either.) But we agree that salvation means taking part in God's nature, being a partner with him in divine life, though never his equal.
Of course, these two ways of understanding salvation, though different, are not mutually exclusive. No one could participate in divine life without having been cleansed from sin. As the Book of Mormon teaches, "no unclean thing can inherit the kingdom of heaven" (Alma 11:37), the ultimate place of divine life. Though the Bible doesn't specifically say the same thing, it subscribes to the same teaching. (See, for example, Eph. 5:5.)
Presumably the reverse is also true: no one cleansed from sin would fail to live the divine life. Nevertheless, the two views of salvation are not the same and the difference makes a difference.
Christians seldom talk much about this particular disagreement, but the positions taken make a big difference in the self-understanding of each group, as well as in the way each understands the other—even though the understandings are seldom explicit. On one side of the disagreement we find Christians for whom salvation means justification, God's judgment that the individual is no longer under condemnation. For Christians on the other side, salvation means coming to live the life that God makes possible.
2 Peter tells us that we receive what we need for godly life by knowing Jesus Christ, with the promise that by knowing him we will come to share in his divine nature. Knowledge is key. But for Mormons the knowledge of Jesus Christ is not particularly theoretical or theological.
Jesus tells us that he is the way, the truth, and the life (Jn. 14:6). In John 14:4, Jesus has told his disciples that they know the way to the place he is preparing, the way back to the Father. They know that way because they know him as a friend, teacher, and exemplar.
Being the way to the Father is not something that Jesus is in virtue of a particular gnosis that he imparts to his followers. He is the way because he gave his life for us. He is the way in view of the fact that we can return to him because of what he has done in the Garden of Gethsemane and on Calvary. He is the way in and through the life he lived and lives, a life we can know as one knows the life of a friend or lover.
Jesus Christ is the truth because he is a revelation of the Father. To know him is to know the Father (Jn. 14:7-9). But knowing the Father through him does not mean knowing truths about the Father. It means knowing the person of Jesus the Messiah and, therefore, also the person of the Father. The knowledge of God is the intimate acquaintance of persons. It is like the knowledge of friends and lovers rather than the knowledge of facts.
As the revelation of the Father, Jesus is the life. In answer to Thomas's question (which amounts to "How will we live if you are no longer here to lead us?" [Jn. 14:5]), Jesus replies that he is the fount of Thomas's life, its way and its truth. The path of the Christian, the way to life in the presence of the Father, is defined by Christ alive in us.
His life shows us the way and the truth of our lives. So if we wish to be with him, we must live the life he has shown us. Knowing him intimately, as one who loves and follows him, means living the divine life, a life that he makes possible and through which he has preceded us.
Understanding salvation in these terms, Mormons do not spend a lot of time concerned about teaching true belief. In fact, in Mormon preaching and teaching there is little that most people would recognize as instruction in divine life. The concerns of our sermons are more often practical than doctrinal: visit those you've been assigned to visit; fast and pray; help your neighbors; go on missions; study the scriptures; care for your families and teach your children; be a good citizen.