The Design Document will be the starting point work product for a number of your assignments.  In many cases you could, and should, do the Design Document before doing any of the actual “work”.  To a degree, the Design Document could be seen a part of the Plan on what you will do, but I tend to look at the Design Document as providing more of a technical overview and the Plan as a second document which includes assumptions, justifications, and the like necessary for meeting the customer’s requirements.  The Implementation then would be the final step, in which you detail exactly – often in a step-by-step manner – what you did to actually complete the work required by the Design Document and Plan.