A test strategy is more inclusive compared to a test plan. A test strategy is completed by a project manager, while a testing manager does a test plan. Test strategy hypothesizes through the general approach, while the test plan is more about the specifics. The testing manager is a mid-level position that requires a person who is on the ball concerning the part with which he is working.
On the other hand, the test strategy is done by someone in a position of power since it requires someone with a strong view of the project. Test strategy encompasses a wide range of components, while the test plan only covers reasonable opinions on the best way to approach the testing.
Another difference between a test plan and test strategy is how they exist over time. The test strategy is a static document that remains the same from start to finish.