Below are three sites discussing Mercy and Grace.
Mercy is unwarranted forgiveness. Grace is unwarranted favoritism.
To summarize the difference: mercy is God not punishing us as our sins deserve, and grace is God blessing us despite the fact that we do not deserve it. Mercy is deliverance from judgment. Grace is extending kindness to the unworthy.
In short, mercy is God not giving us what we do deserve; grace is God giving us something we do not deserve.
Grace: According to dictionary.com “grace” is defined as the manifestation of favor by a superior. It can also be defined as the freely given, unmerited favor and love of God. In very few words, grace is getting what you do not deserve.
Mercy: According to dictionary.com the term “mercy” can be defined as having a disposition of compassion or forbearance (to refrain from something).