What's the difference between data mining and data warehousing, databases, querying, etc.?

Data mining is fundamentally an analytical, statistical process. Querying databases is a completely distinct function with a well-defined user query/machine response loop.

In data mining, one typically deals with data which is already prepared as a single table (or at least abstractly, as a single relational database query), and the goal is to have the computer discover patterns in the data, as models, segments, etc. Input: "all" of the data (or a statistical sample), output: the discovered patterns.

Querying, on the other hand involves user specification of a subset of the data to be retrieved. Input: query specification, output: relevant data set.

While data mining may involve querying (especially to extract the relevant statistical sample), and querying may be driven by things discovered during data mining, these are seperate processes.