Simple.
A chest rig is designed to carry the kit, like ammo, med kits and tools. The mission specific gear you need carried in a location that's easy to access under stress.
A plate carrier is designed to carry armor. Some are "armor carriers" capable of carrying soft armor AND hard plates, some just carry the hard plates.
Plate carriers can be had in low profile "slick" styles with no ability to attach pouches to MOLLE/PALS points, or in full MOLLE/PALS compatible styles so you can attach your pouches directly to the carriers. Depending on your mission or job, you may indeed find a need to wear a chest rig (rack) over a plate carrier, such as times when you need full protection without a complete load out. Carriers with full MOLLE/PALS are more money, but offer more versatility. Rack over it, or attach your load directly, depending on your mission.
If you never need armor, just get a chest rig. Do NOT buy a plate carrier, then load out without plates. People will look at you funny, and it just won't function well.