I am not a complete literate when it comes to processing natural language.
So, wondering whether they are same or not?
This is just my opinion, but I think of "text mining" when I think of search and retrieval mostly, but also document clustering and topic modeling. "Natural language processing" to me includes translation, sentiment analysis and entity recognition. I think they can reasonably considered different, but they overlap. You're welcome to try to list some key features of each based on a discussion here in tag descriptions here.
Added a post regarding the same on the main site with my understanding about the two domains.