[daniel1212]

God sets us apart (holiness). God makes us walk with Him (righteousness). And God makes us trust in Him (godliness).

Indeed, but holiness is also practical, not only righteousness. It may be that holiness is more that of being pure, distant from sin, due to being righteousness in abstaining from and overcoming it.

The question is asked due to,

He that is unjust, let him be unjust still: and he which is filthy, let him be filthy still: and he that is righteous, let him be righteous still: and he that is holy [hagios], let him be holy [hagiazō] still. (Rev 22:11)

[HarleyD]

Indeed, but holiness is also practical, not only righteousness. It may be that holiness is more that of being pure, distant from sin,

I'm sorry but I don't see that in scripture or the commentaries. Holiness means "set apart". Thus you have the holy temple, holy ground that Moses walked on, the holy of holies, the holy scriptures, and a holy nation to name but a few. These items are set apart by God and only God can declared something holy. Even God is a holy God-set apart from us. It isn't a distance. It is a separation. And whenever holy is used in scripture it means a separation from something else.

Righteousness is sanctification which God leads all believers for His glory and honor:

Psa 23:3 He restores my soul. He leads me in paths of righteousness for his name's sake.

Thus Revelation:

He that is unjust, let him be unjust still: and he which is filthy, let him be filthy still: and he that is righteous, let him be righteous still: and he that is holy [hagios], let him be holy [hagiazō] still. (Rev 22:11)

Righteousness is sanctification. Holiness is justification.