A.W. Pink notes the differences between sanctification and justification in his book The Doctrine of Sanctification: Discerning real and false notions of Holiness. Here’s a lengthy, but very good, quote from Chapter 2, “Its Meaning”:
“Though absolutely inseparable, yet these two great blessings of divine grace are quite distinct. In sanctification something is actually imparted to us, in justification it is only imputed. Justification is based entirely upon the work Christ wrought for us, sanctification is principally a work wrought in us. Justification respects its object in a legal sense and terminates in a relative change—a deliverance from punishment, a right to the reward; sanctification regards its object in a moral sense, and terminates in an experimental change both in character and conduct—imparting a love for God, capacity to worship him acceptably, and a meetness for heaven. Justification is by a righteousness without us, sanctification is by a holiness wrought in us. Justification is by Christ as Priest, and has regard to the penalty of sin; sanctification is by Christ as King, and has regard to the dominion of sin: the former cancels its damning power, the latter delivers from its reigning power.
They differ, then, in their order (not of time, but in their nature), justification preceding, sanctification following: the sinner is pardoned and restored to God’s favour before the Spirit is given to renew him after his image. They differ in their design: justification removes the obligation unto punishment; sanctification cleanses from pollution. They differ in their form: justification is a judicial act, by which the sinner is pronounced righteous; sanctification is a moral work, by which the sinner is made holy: the one has to do solely with our standing before God, the other chiefly concerns our state. They differ in their cause: the one issuing form the merits of Christ’s satisfaction, the other proceeding from the efficacy of the same. They differ in their end: the one bestowing a title to everlasting glory, the other being the highway which conducts us thither. ‘And an highway shall be there, …and it shall be called The way of holiness’ (Isa. 35:8).”