You can look at planning at different levels:

• strategic planning is about making long term plans for your business as a whole, based on your vision and mission and often looking 2+ years ahead in time
• other levels of planning are:
• tactical planning which typically focuses on making plans for shorter periods of time, like 1-2 years, and for specific parts of the business, e.g. production, marketing, personnel etc. The tactical plans should of course be related to the strategic plan.
• operational planning which is about planning the daily tasks in the business in order for the business to reach the goals of the tactical plans, and ultimately the strategic plan.

Projects are different because they are characterized by being:

• temporary, in that they have a defined beginning and end, and therefore they are also defined in scope 
• unique, in that they are not routine operations but a specific set of operations designed to reach a specific goal, likely some kind of change

You can consider the process of starting a business as a project in itself - and after starting the business, you may need to implement many changes along the way which can also be dealt with as projects.