In nuce: The sanctification is the divine imperative "Ye shall be my people" while justification is the divine indicative "I want to be your God".

Luther

Martin Luther and later the Lutherans focus on the doctrine of justification by faith alone. Is that all? "No" they say – there's also sanctification: true faith is manifested in the works. But as soon as having said that, they are in a hurry to come back to the justification.¹ Luther also talks of works, but immediately, when he does, he takes a step back and insists on: "The works do nothing for justification".

^{1: Eberhard Busch, Meine Zeit mit Karl Barth: Tagebuch 1965-1968 (2011), 325}

Calvin

Peculiar to Calvin is the narrowness of entanglement between justification and sanctification: Against the contempt of work.

From God's perspective, justification and sanctification are the duplex gratia and will be given only together – but nevertheless they have to be clearly seperated.¹

In his "Institutio", Calvin deals first with sanctification and then with justification. This doesn't say that justification is in any way less worth, but it highlights that there won't be a iustificatio without a sanctificatio. The justification has to be believed and held in faith, while the sanctification is the real life issue which permeates the daily experience.²

Calvin doesn't think of the Christ as a sinner, but rather as a reborn, who's already unter the sanctification of God – given by the Holy Spirit. The grace of justification accompanies the reborns fight against the flesh on the way to his sanctification until death.

^{1: Inst.III,16,1: Nullum ergo Christus iustificat quem non simul sanctificat. Sunt enim perpetuo et individuo nexu coniuncta haec benificia … Inter se distinguamus licet, inseperabiliter tamen utranque Christus in se continet
2: Karin Bornkamm, Christus – König und Priester, 1998 J.C.B. Mohr, Tübingen, 319ff.}

Biblical Evidence

The ethical passage Gal 5:13 – 6:10

^5:13You, my brothers, were called to be free. But do not use your freedom to indulge the sinful nature; rather, serve one another in love. [...] ²² But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, ²³ gentleness and self-control. [...] ^6:8The one who sows to please his sinful nature, from that nature will reap destruction; the one who sows to please the Spirit, from the Spirit will reap eternal life. ⁹Let us not become weary in doing good, for at the proper time we will reap a harvest if we do not give up.

This makes clear: The freedom from the law (i.e. justification) doesn't mean freedom for the flesh, but rather a calling to charity. The faith must be active in charity.¹

Sanctification as the goal of new life: Rom 6:19 and 22

¹⁹I put this in human terms because you are weak in your natural selves. Just as you used to offer the parts of your body in slavery to impurity and to ever-increasing wickedness, so now offer them in slavery to righteousness leading to holiness. [...]²²But now that you have been set free from sin and have become slaves to God, the benefit you reap leads to holiness, and the result is eternal life.

In both verses an εἰς ἀγιάσμος (to holiness) can be found as the goal of this "new life" (Rom 6:4).²

and so on

• 1 Thess 2:10
• 1 Kor 1:30; 6:11
• 2 Kor 6:14ff.

Please note that in all those passages, the terminology of sanctification and righteousness is used parallel.²

^{1: Cilliers Breytenbach (ed.), ''Paulus, die Evangelien und das Urchristentum'', 2004 BRILL, 170f.
2: Martin Vahrenhorst, Kultische Sprache in den Paulusbriefen, 2009 J.C.B. Mohr, 279}