Test Strategy is more of a high level document discussing and giving information on What the QA group will do on a project, the Test Plan is a low level detailed document that goes over How things will be done. Often the Test Strategy is done, in my experience, when the project is kicked off and you only have a rough outline on what will be built, so you need to show What will be done, with What tools and with What resources. Again the focus on the What. The Test Plan comes when you have more detail, and gets more as code is built and later design decisions are made, so this will cover more on How things will be tested and give an idea of the Test Cases that will be executed.

I largely concur with Michael but wil add a point or two. The test strategy is needed early on to make descisions about the staffing levels and calendar time needed to complete the testing tasks of the project as well as influence testing staff selection. The details of the exact tests and detailed planning for the exact tests can wait but typically scoping things out well enough to make sound staffing and schedule decisions cannot wait. Some examples of high-level test strategy questions are: Are we going to use automated regression testing tools and which ones? Which OS and user interface environments are we going to test? Are we going use an orthogonal array or similar approach? Emphasis on black box versus white box? etc. I find the "what" vs. "how" dichotomy used above useful as a stepping stone but ultimately a little artificial. I prefer the "needed early on" vs. "can be deferred a bit " distinction but that is a minor point and the words are certainly not as catchy as what vs. how..