Strategy and planning are two terms that mean essentially the same thing except for their timeframe. Strategy is the business vision that is currently being executed and planning is the long term vision of how the business vision will be executed.
Many times for smaller businesses, planning is not formally mapped out and the current strategy is by default however the current businerss operates. At larger businesses, the vision and excution of strategy and planning falls on upper management. In public companies, CEOs will be hired and fired for their performance in this area.