Grace…mercy, what’s the difference?

I recently began to wonder what the difference between God’s mercy and God’s grace is. I mean, the reason I am saved is because of God’s grace…so is mercy and grace interchangeable or does God practice grace on those who believe because of His great mercy?

I looked up the two words in Webster’s Dictionary and here are the applicable definitions:

Mercy:
1 a: compassion or forbearance shown especially to an offender or to one subject to one’s power; also: lenient or compassionate treatment
2 a: a blessing that is an act of divine favor or compassion

Grace:
1 a: unmerited divine assistance given humans for their regeneration or sanctification
   b: a virtue coming from God
   c: a state of sanctification enjoyed through divine grace

Well there we go.

God regenerates and sanctities those who have faith in Him through the propitiation of our sins by the blood of His son Jesus because of His compassion, forbearance and divine favor on the offenders (us) who are subject to His power.

Romans 3:21-30
But now apart from the Law the righteousness of God has been manifested, being witnessed by the Law and the Prophets, even the righteousness of God through faith in Jesus Christ for all those who believe; for there is no distinction; for all have sinned and fall short of the glory of God, being justified as a gift by His grace through the redemption which is in Christ Jesus; whom God displayed publicly as a propitiation in His blood through faith. This was to demonstrate His righteousness, because in the forbearance of God He passed over the sins previously committed; for the demonstration, I say, of His righteousness at the present time, so that He would be just and the justifier of the one who has faith in Jesus.

Where then is boasting? It is excluded. By what kind of law? Of works? No, but by a law of faith. For we maintain that a man is justified by faith apart from works of the Law. Or is God the God of Jews only? Is He not the God of Gentiles also? Yes, of Gentiles also, since indeed God who will justify the circumcised by faith and the uncircumcised through faith is one.

Do we then nullify the Law through faith? May it never be! On the contrary, we establish the Law.

Hebrews 2:9-17
But we do see Him who was made for a little while lower than the angels, namely, Jesus,because of the suffering of death crowned with glory and honor, so that by the grace of God He might taste death for everyone.

For it was fitting for Him, for whom are all things, and through whom are all things, in bringing many sons to glory, to perfect the author of their salvation through sufferings. For both He who sanctifies and those who are sanctified are all from one Father; for which reason He is not ashamed to call them brethren, saying,

“I WILL PROCLAIM YOUR NAME TO MY BRETHREN,
IN THE MIDST OF THE CONGREGATION I WILL SING YOUR PRAISE.”

And again,

“I WILL PUT MY TRUST IN HIM.”

And again,

“BEHOLD, I AND THE CHILDREN WHOM GOD HAS GIVEN ME.”

Therefore, since the children share in flesh and blood, He Himself likewise also partook of the same, that through death He might render powerless him who had the power of death, that is, the devil, and might free those who through fear of death were subject to slavery all their lives. For assuredly He does not give help to angels, but He gives help to the descendant of Abraham. Therefore, He had to be made like His brethren in all things, so that He might become a merciful and faithful high priest in things pertaining to God, to make propitiation for the sins of the people.