I find that the terminology associated with specialized fields like data mining very interesting to track. My first boss, Roger Barron (better described as a mentor and later truly a friend--I owe much of who I am as a professional to him), used to talk of the transitions of terminology in technology: bionics, cybernetics, artificial intelligence, neural networks, etc.
I find that data mining and predictive analytics fall into the same category--they are the same basic technology but described from different perspectives. Sometimes colleagues have tried to point out distinctions, and I think one of the better ones was posted by Eric King here, where my definition of "better" means simple and clear.
Predictive analytics is a term I see more in the CRM and database worlds (TDWI conferences come to mind). Perhaps some of this is due to the encroachment of BI into the data mining world, where queries and OLAP are sometimes called data mining (after all, you are "drilling" down into the data!). This would necessitate creating further distinctions in terminology.
However, I don't see data mining losing hold on the style of predictive modeling that is largely empirical and data driven. So I include predictive analytics in the title of this blog as an alternative to data mining in name only, not in purpose.