Another way to look at it is that a company should have a test METHODOLOGY ( expressed in an easy to follow public document) that it applies to each project.
This is the set of steps to be followed and the artifacts (documents, results, paper copies, data sets, etc) that are required for successful testing / QA of the project and hand over to production.
One of the first steps in that methodology is ususally to develop the test STRATEGY for that specific project. This is the approach to be taken given the technology involved and things like timing, resources, environments, phases, duties, etc.
As such, a test strategy is a component of an effective test methodology, as it is applied to a specific project.
Hope this helps (and doesnt start a post-storm)
"Not every solution was derived to address an obvious problem" - Me (quite recently indeed)