Planning is when you start with a goal in mind. Then you break it down into "what do I need to do to achieve that goal", with timelines. Such as today I will plan my meals for the week. Tomorrow morning, I will go out and get the groceries I need. And by tomorrow night, all the veggies will be in easy to use baggies, ready to go.
Worrying would be more of the "but what if" types of things. What if I don't eat all my meals at home this week, will the groceries spoil? What if I forget my list at home?
I guess the planning helps you to achieve the goal, while the worrying starts you thinking about what happens when an obstacle appears in your path (cause we all know they can appear out of no where).
Does this help?