To oversimplify things a bit, Mormon notions of salvation are more consistent with Paul, while Evangelical notions of salvation are more consistent with deutero-Pauline ideas. In essence, Mormons, like Paul, believe that salvation is a future event; while Evangelicals, like deutero-Pauline authors, believe that salvation is a present event.
The deutero-Pauline letter Ephesians claims, “by grace you have been saved” (Eph 2:5, NRSV). The deutero-Pauline text Colossians agrees, and goes even further, explaining that you have died and have been raised already (Col 3:1-3). Saved in the past tense? Already raised? Yes, these texts consider that it is at baptism or some other event that has already brought about salvation.
In the genuine Pauline letters, “salvation” and “save” are only used in the future tense. If you asked Paul, “have you been saved,” he would say, “no.” For Paul, salvation came either after death or with the (impending) coming of the Lord. One could not claim to be saved yet, not because of an insecurity about one’s status before the Lord, but simply because salvation had not yet come.
The question of whether salvation was a present or future event was of great concern in early Christianity. The same tension may be found in the sayings of Jesus concerning the coming of the Kingdom. For some sayings, the Kingdom was a future event, either after death or precipitated by some cosmic occurrence. For others, “the Kingdom of God is among you” (Luke 17:20-21). Other deutero-Pauline epistles like 2 Thess try to warn against presentist understandings of the coming of the Lord, chastizing those who have quit their jobs, urging the readers “not to be quickly shaken in mind…that the day of the Lord is already here.” (2 Thess 2:2).
For what it’s worth, the Book of Mormon seems to be aware of this tension within the Pauline (including deutero-Pauline) corpus. In fact, the most famous Book of Mormon text on grace and salvation is really a commentary on Eph 2:5: “by grace ye are saved.” (KJV). 2 Nephi 25:23 interprets this past tense notion of being saved as a conditional: “by grace that we are saved, after all we can do.” The near quotation of Eph 2:5 in Nephi’s formulation suggests that this text is best understood as a commentary on Eph 2:5. The main thrust of Nephi’s point is to reconcile the present-oriented understanding of salvation in the deutero-Pauline epistles with the future-oriented Pauline theology. Mormon notions of salvation derive from this Pauline view.