Grace is often defined as "unmerited favor."  If mercy is not getting what you do deserve, then grace is going one step further and getting what you don't deserve.  A child is shown mercy when the parent chooses not to punish the child for disobedient behavior.  Perhaps the consequences of the disobedient choice were sufficient for correction in the parent's wisdom.  A child is shown grace as the parent continues to love and nurture a child making disobdient choices with hopes that time and truth will eventually result in maturity and better choices. 

So it is with God.  Sinful human beings are not only given mercy but grace by which God exchanges our sin for eternal life with Him.