First, I'm going to directly quote the two tags you put on this question:
The data-mining tag says:
Data mining is the process of analyzing large amounts of data in order to find patterns and commonalities.
The pattern-recognition tag says:
Pattern recognition is the term given to the science of automating the classification of input into pre-determined categories, or on the other hand, of being able to recognise particular categories of input by their characteristics.
Now, irony aside, the way I've always seen it is that in data mining you don't necessarily know the patterns. You have to look for them, which can often involve a lot of hunch-following and guess-work combined with a bit of solid testing.
In pattern-matching, you tend to know the patterns already and you search for them based on their features.