Strategy is planning, it's the art and some science of planning and directing large scale operations. This is the 'WHAT' and not necessarily the 'HOW'.
No two situations are the same, using comprehension and questioning to refine understanding assists with this - bringing expose, experience and education together.
Without understanding the end product planning can come in several flavours - where requirements are not clear agile planning can play a role.
Management is doing, it involves tried and tested methods and sequencing of resources, tools and techniques to gain an end goal or result.