In my opinion, there is none. If you graduated with a degree in stats, you call it computational statistics. If you graduated with a degree in computer science, you call it data mining. In both cases, it's about processing large data sets using statistical techniques. Do you have a different opinion?
Re the idea of meaninglessness: Blind signal processing is the analysis of data in which one doesn't know what components are there, or their meanings. In contrast, recognition techniques such as speech recognition and pattern recognitioni are used when one is searching for particular features.
I allways thought there was a huge difference, you know but now Im not so sure, I am assisting with a 'Random Forrest' implementation right now, its a bit off-piste for me, athough ironically a long time ago I was involved in early data mining experiments which were not as methodologically sound as they are today. Anyway implementing this Random Forrests application makes clear to me that not only from the technology perspective but also in terms of the math and the visualisation potential, data mining and statistical computing are asymptotic to use an odd metaphor. There are other current trends pointing that way, particularly in the 'semantic integration' and optimised search space, in my view; for what its worth.
I feel "data mining" is nothing but "data analytics" aided by "computational statistics" . You need both to actually mine for knowledge. For instance, Market Basket Analysis is a type of data analytic which requires computational statistics such as Probabililty and Regression measures to beget knowledge.