What is the difference between data mining and statistical analysis?

For some background, my statistical education has been, I think, rather traditional. A specific question is posited, research is designed, and data are collected and analyzed to offer some insight on that question. As a result, I've always been skeptical of what I considered "data dredging", i.e. looking for patterns in a large dataset and using these patterns to draw conclusions. I tend to associate the latter with data-mining and have always considered this somewhat unprincipled (along with things like algorithmic variable selection routines).

Nonetheless, there is a large and growing literature on data mining. Often, I see this label referring to specific techniques like clustering, tree-based classification, etc. Yet, at least from my perspective, these techniques can be "set loose" on a set of data or used in a structured way to address a question. I'd call the former data mining and the latter statistical analysis.

I work in academic administration and have been asked to do some "data mining" to identify issues and opportunities. Consistent with my background, my first questions were: what do you want to learn and what are the things that you think contribute to issue? From their response, it was clear that me and the person asking the question had different ideas on the nature and value of data mining.