Righteousness is right standing and right living
In the Bible, righteousness has to do with what is right, just, and faithful before God. It can describe God's own perfect character, his fair judgement, and the way he wants people to treat him and one another.
For Christians, righteousness begins with a gift rather than a personal achievement. Paul explains that people are made right with God through faith in Jesus Christ, not by earning a place through religious effort (Romans 3:21-22). He also says that Christ took the sin of his people so that they might receive God's righteousness in him (2 Corinthians 5:21).
That gift changes the direction of a life. Righteousness is not merely a label on paper. It leads someone to turn from dishonesty, bitterness, sexual wrongdoing, and injustice, and to pursue truth, mercy, faithfulness, and love.
Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference:
Holiness means belonging to God
Holiness means being set apart for God. God is holy in a unique and complete sense, utterly pure and unlike anything he has made. When he calls people holy, he is saying that they belong to him and are meant to reflect his character.
Peter writes to ordinary Christians scattered through several regions of the Roman world and calls them to be holy in the whole shape of their conduct (1 Peter 1:15-16). This is not a call to withdraw from people or pretend to be flawless. It is a call to live as God's people in the places where they already are.
The New Testament often uses the word sanctification for this growing holiness. Paul says that God's will includes believers being sanctified, turning away from sexual sin and learning self-control that honours God (1 Thessalonians 4:3-4).
But as he which hath called you is holy, so be ye holy in all manner of conversation;
They are different, but they belong together
A simple way to distinguish them is this: righteousness focuses on being right with God and doing what is right, while holiness focuses on belonging to God and being formed by his purity. Righteousness asks, “What is faithful and just?” Holiness asks, “Does this fit the life of someone who belongs to God?”
Still, Scripture does not pull them apart. Paul links righteousness with holiness when he tells believers to put on the new person, created according to God in true righteousness and holiness (Ephesians 4:24). A person cannot treat holiness as private spirituality while ignoring honesty or justice. Nor can they pursue outwardly right behaviour while refusing God's claim on their life.
And that ye put on the new man, which after God is created in righteousness and true holiness.
Growing without pretending
Christians are called to pursue holiness, but that pursuit does not mean they have already arrived. Hebrews urges believers to seek peace and holiness, while the rest of the New Testament shows that growth takes time, repentance, prayer, and the help of God's people (Hebrews 12:14).
So if you trust Christ, you do not need to prove your worthiness before coming to God. Receive his mercy, then ask him to shape your choices. Read the passages around these verses slowly. Notice both the comfort and the invitation: God makes his people right with him, and he patiently teaches them to live as his holy people.