In short:
Plan - Overall big picture... i.e. How big is the market, who are your clients/customers, what is your USP compared to competition, projections for next x months / years etc.
What are the goals and expectations at each set period.
Strategy - How you are going to achieve the goals set out in the plan, defined milestones, measurements and reporting, specific actions related to milestones, contingencies for each element. Actions required to achieve the projected results in the plan and a planned project timetable.
What specific actions are required to achieve the goals and milestones.
It's vastly more complex than that of course, and it entirely depends on what the purpose you're writing them is.