Question: In *[The Path of the Just](http://rads.stackoverflow.com/amzn/click/1583306773)* (Mesilat Yesharim) by [Rabbi Moshe Chaim Luzzato](https://en.wikipedia.org/wiki/Moshe_Chaim_Luzzatto) (ch.19), I noticed he sometimes uses the term "nachat ruach" and other times "korat ruach." 

What is the meaning of both expressions and their distinction in this context?

Answer: 
In kesubos 40b the gemara explains that a rapist has to pay the raped woman damages (פגם) based on the her loss in value, which is estimated by how much a person would pay more for a virgin slave woman to marry her off to a slave that gives him korat ruach. Rashi says that because the slave gave him korat ruach the master wants to give him nachas ruach by marrying him off to virgin.

It appears from here that korat ruach is needed to cool down a person who is angry or worried. Nachas ruach seems to be relevant when a person has a desire for something, his ruach isn't quiet until he gets it. This last point is spoken out by the GRA on Mishlei 1:23. The concept of ruach is really a kabalistic concept (נר"נ - נשמה רוח ונפש) and is spoken about extensively by the GRA in Mishlei, and many other books.
Both terms are present in Mishnaic literature. The Mahzor Vitry (427) writes that the terms carry the same meaning; calmness:

> 
> שאין כאן קורת רוח שלימה. קורת רוח. נחת רוח. לשון נתקררה דעתו. וכלפי שהחרון אף ועצבת רוח נקרא חימה. הרצון והנחת רוח נקרא קורת. שמתקררת ומיישבת דעתו עליו מרוב שמחה והנאה 
> 
> 
> That there is not a complete "korat ruah". 'Korat ruah': 'nahat ruah'. An expression of of calming [lit. cooling] oneself down. And this corresponds to anger and disturbance of spirit is called 'heimah'[lit. heating], 'ratson' and 'nahat ruah' [a settled spirit] is called 'korat' [literally cooled], for it cools and settles a person's mind from an abundance of happiness and pleasure.
> 
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Obviously every writer can use words differently...