Test strategy is a part of test plan.
For example Test strategy is types of testing like System Test,Functional Test,Performance Test,Security Test,Automated Test,tress and Volume Test ,Recovery Test ,Documentation Test ,User Acceptance Test,Compatibility Test,Usability Test ,Interface Test---etc.
Test plan is a detailed understanding of what the eventual work flow will be like Introduction,Scope,Test Strategy,Environment Requirements,Test Schedule,Control Procedures,Functions To Be Tested,Resources and Responsibilities,Deliverables, Suspension / Exit Criteria,Resumption Criteria,Dependencies,Risks,Tools,Documentation,Approvals---etc.
Test stratergy includes many other stuffs. It includes what u are going to test, how you are going to test, what time duration u are going to take to test it , how many resource getting involved what is the risk involved and clear idea of the scope of that testing