What is the difference between holiness and righteousness? Both holiness and righteousness are used to describe God.  Additionally, we as Christians are called to be holy and righteous as well.  These are two distinct words, so they must have distinct meanings.

So, my question is what distinguishes holiness from righteousness?


  You shall be holy to me, for I the Lord am holy and have separated you
  from the peoples, that you should be mine.  Leviticus 20:26 ESV
  
  14 As obedient children, do not be conformed to the passions of your
  former ignorance, 15 but as he who called you is holy, you also be
  holy in all your conduct, 16 since it is written, “You shall be holy,
  for I am holy.”  1 Peter 1:14-16 ESV
  
  You are witnesses, and God also, how holy and righteous and blameless
  was our conduct toward you believers.  1 Thessalonians 2:10 ESV
  
  But that is not the way you learned Christ!— 21 assuming that you have
  heard about him and were taught in him, as the truth is in Jesus, 22
  to put off your old self,[f] which belongs to your former manner of
  life and is corrupt through deceitful desires, 23 and to be renewed in
  the spirit of your minds, 24 and to put on the new self, created after
  the likeness of God in true righteousness and holiness.  Ephesians
  4:20-24 ESV
"Holy" means "set apart", as in set aside for a particular purpose, and implies being "special" and acting accordingly. In particular it means "set aside for God's service".

"Righteous" means "made right" (justified), or "being right", not in the sense of "correct", but as in "not wrong" - being pure, honest, sinless. Perhaps a better way of putting it would be "not guilty" or "blameless".

The two should go hand in hand.