God's mercy covers our past sins, but God's grace does more than that - God's grace teaches us something. The very word teaches implies that God still has principles, or laws, even after the annulling of the Old Covenant. And what does God's grace teach us?
"For the grace of God that bringeth salvation hath appeared to all men [we like that part], teaching us that, denying ungodliness and worldly lusts, we should live soberly, righteously, and godly, in this present world..." (Titus 2:11,12)
God's grace powerfully does for us what the Law was unable to do because of our weakness.