All religions have their own focus on righteousness. Only Christianity presents two different kinds of righteousness.
Vertical Righteousness
Vertical righteousness (also called positional righteousness) is the righteousness between us and God.
Martin Luther called it an “alien righteousness.” Not that it comes in a UFO, but that it comes to us from outside ourselves. We can't produce this righteousness. We are dead in sin! So Christ obtains this righteousness for us. Jesus' perfect life, death, and resurrection secure for us an eternally perfect standing with God. We are forever righteous in His sight.
Vertical righteousness is therefore a passive righteousness –– we don't earn it, it's God's free gift of grace that we receive through faith at the moment of our conversion.
Scriptural examples:
“For our sake he made him [Christ] to be sin who knew no sin, so that in him we might become the righteousness of God" (2 Cor 5:21).
“And to the one who does not work but believes in him who justifies the ungodly, his faith is counted as righteousness” (Rom 4:4-5).
“I am in him, not having a righteousness of my own that comes from the law, but that which comes through faith in Christ, the righteousness from God that depends on faith” (Phil 3.8-9).
Horizontal Righteousness
Horizontal righteousness (also called practical righteousness) is the righteousness between us and our fellow man.
This is an active righteousness where we serve our neighbors in gentleness and love.
Scriptural examples:
“Be completely humble and gentle; be patient, bearing with one another in love” (Eph 4:2).
"Let your conversation be always full of grace, seasoned with salt, so that you may know how to answer everyone" (Col 4:6).
“Make sure that nobody pays back wrong for wrong, but always strive to do what is good for each other and for everyone else” (1 Ths 5:15).
How They Relate
Many Christians (and pastors) don't even know that there are two kinds of righteousness and so they mix the two together, which causes much anxiety/self-righteousness. We must instead keep them separate. As Egon warns in Ghostbusters: "Never cross the streams!"
This is so critical.
Our horizontal righteousness never effects our vertical righteousness. We've been gifted Jesus’ perfect righteousness by grace and can neither diminish it nor improve upon it. EVER. It's permanent.
Therefore, our good works don't merit us favor with God and our bad works don't remove God's favor from us. Horizontal righteousness then is not for God's benefit. How could it be? In His eyes we already have Jesus' perfect righteousness!
So what's the point of good works?
Luther: “God doesn’t need our good works, our neighbor does.” Horizontal righteousness is for our neighbor's benefit, that he might see our good works and worship God (Mt 5:16).
BUT! Though the horizontal never effects the vertical, the vertical has a profound effect on the horizontal. The kind and gracious way Jesus treated us will naturally have a positive impact on the way we treat our neighbors.
"But by the grace of God I am what I am, and his grace to me was not without effect. No, I worked harder than all of them—yet not I, but the grace of God that was with me" (1 Cor 15:10).
For Further Reading