A wedding designer doesn't plan a wedding, he designs it.
The wedding planner has to plan every single details of the wedding : guests, outfits, ceremony, reception, food, drinks, music, photos, wedding cake... He's the wedding coordinator.
Whereas the wedding designer is in charge of the decoration only. Also, some wedding planners take care of the decoration too. As I do. It can be less expensive if the wedding planner is in charge of everything.
I hope it can help you.
Johanna, Cherry Wedding : wedding planner Paris