In Christianity, it might be very difficult to differentiate between Grace and Mercy since both are often used interchangeably. In fact, most Christians usually argue about the proper usage of these two words. The word "mercy'' is usually discussed in relation to the unfailing love of God that leads sinners to God and heal them of their sins. Most Christians always use the word mercy when asking God to forgive them of their sins.
This is just in line with the English translation of the word "Mercy," i.e., compassion or forgiveness, especially toward a criminal or offender. On the other hand, grace means a free and undeserved favor from God, especially one that grants divine assistance to humans for their sanctification. Although, there is more to what grace entails, the meaning has been abused by so many people, thinking it is a free license to start living a wayward life.