Strategy planing includes planning and defining the strategy, goal and direction of the business and the processes. So in our case when I am a project manager for large online retailer and make plan for new arm of the business, strategic planning would involve answering the question: What do we (the business) do and what are our goals, what should we achieve?
Tactical planning is short range planning that defines what every part of the business should do. In this case for example, what are the goals of the marketing team, the billing team, the sales team...
Operational planning includes defining milestones and conditions for success and how the new arm of the business would be put in operation.