Route planning is the entire process that starts from having a list of addresses, creating a multi-stop routes (either manually or use route optimization algorithms), inspecting and editing those routes, all the way to dispatching those routes to your drivers, ideally on their mobile app.
Route optimization is a part of the route planning process, which seeks to automate the process – so you spend less time route planning – and to find the most efficient route possible, thereby cutting mileage and fuel costs.
For more details, see Route Planning vs Route Optimization.