I have a few, but more suggestions are always welcome. Grace is what God offers to fallen sinners through the salvation obtained by the atonement of Jesus Christ. We call it grace because it is undeserved. All these phrases are various theological narrowings of the term grace. Your use of these particular terms will differ depending upon the theological tradition you ally yourself with.
Mercy is what grace offers.
The grace of God comes to us in our poor sinful condition and offers us the mercy of God when we deserve His wrath. So grace comes to us giving us mercy. I admit it is somewhat semantical, and the terms are virtually interchangeable. There is a subtle difference in the two words. Mercy has meaning more synonymous with compassion.