Process Designer is a tool to manage data for manufacturing planning including bills of products, bill of process, part and resource libraries and so on. It also can work in combination with Process Simulate for detailed 3D process simulation. PD requires Oracle as data managed backbone. If you know Teamcenter, PD is some alternative for Teamcenter Manufacturing.
Plant Simulation is a standalone tool for descrete event simulation of different systems (not only manufacturing, but warehouse, transport, logistics and other kinds). The most common task for Plant Simulation is to predict how system will behave (throughput, bottlenecks, prod.cycle, energy consumption etc). Simulation interval is usually much longer then one production cycle (days, weeks, years). And random factors (failures, time distributions etc) are considered.