Consider a few contrasts between them

(Arthur Pink)

"The law was given by Moses, but grace and truth came by Jesus Christ" John 1:17

Law and grace are antithetical terms. Consider a few contrasts between them:

The Law manifests what is in man-sin.
Grace manifests what is in God-love and mercy.

The Law speaks of what man must do for God.
Grace tells of what Christ has done for men.

The Law demands righteousness from men.
Grace brings righteousness from God to men.

The Law brings God's justice to men.
Grace brings men to God's mercy.

The Law sentences a living man to death.
Grace brings a dead man to life.

The Law never had a missionary.
The Gospel is to be preached to every creature.

The Law makes known the will of God.
Grace reveals the heart of God.

Grace is the sinner's only hope. Unless we are saved by grace, we can never be saved at all.

Grace is God's provision for those who are . . .
  so corrupt that they cannot change their own natures;
  so averse to God that they cannot turn to Him;
  so blind that they cannot see Him;
  so deaf that they cannot hear Him;
  so dead in sin that He must open their graves and give them spiritual life, if ever they are to be saved.

Grace implies that the sinner's case is desperate, yet that God is merciful.

"You are not under law, but under grace." Romans 6:14