I agree with Sean's answer.
[NLP][1] and [text mining][2] are usually used for different goals.
Also, there is indeed an overlap and both definitions are vogue.

Other than the difference in goal, there is a difference in methods.
Text mining techniques are usually shallow and do not consider the text structure. Usually, text mining will use bag-of-words, n-grams and possibly stemming over that.

In NLP methods usually involve the text structure. You can find there sentence splitting, part-of-speech tagging and parse tree construction. Also, NLP methods provide several techniques to capture context and meaning from text.
 
Typical text mining method will consider the following sentences to indicate happiness while typical NLP methods detect that they are not

 1. I am not happy
 2. I will be happy when it will rain
 3. If it will rain, I'll be happy.
 4. She asked whether I am happy
 5. Are you happy?

 [1]: https://en.wikipedia.org/wiki/Natural_language_processing
 [2]: https://en.wikipedia.org/wiki/Text_mining