Just another point of view, Dig the topic names a bit deeper.
Text mining - mining of text (just as data mining, and the data is text data). mining is about extracting useful information from the available data. information could be patterns in text or matching structure but the semantics in the text is not considered. The goal is not about making the system understand what does the text conveys, rather about providing information to the user based on a certain step by step process.
Natural language processing - Natural language is what humans use for communication. processing such a data is NLP. The data could be speech or text. Thus, the main goal is towards understanding what is the semantic meaning conveyed in it. Now you know why we care about grammatical part of speeches and the lexical relations among them.
speech recognition systems could be a part of NLP, but it has nothing to do with text mining. And, it seems like NLP is the bigger fish and it uses text-mining, but its actually the other way around. text-mining uses NLP, because it makes sense to mine the data when you understand the data semantically.