A "scoffer" in this context is one who mocks Christ, ridicules the things of God, and opposes the gospel. Both Peter and Jude were writing warnings against false teachers who were intent on leading others astray. The word scoffer refers to one who denies the truths of Scripture and entices others to go along with his error.
The word unbeliever was understood to represent everything opposed to Christian faith and godliness. In 2 Corinthians 6:14–15, Paul writes, "Do not be bound together with unbelievers; for what partnership have righteousness and lawlessness, or what fellowship has light with darkness? Or what harmony has Christ with Belial, or what has a believer in common with an unbeliever?" The understanding was that those who had come to faith in Christ were in the process of being transformed into the image of Jesus (Romans 8:29). The further along they were in this process, the fewer similarities they had with unbelievers.