There's a trade-off between weight/mobility and protection. Usually, heavier the armor, the more it protects. Most front-back vest type only protects against regular 9mm pistol rounds. To offer more protection, you need ballsitic plates (metal or ceramic) as inserts and that adds weight.
Furthermore, different armor differs in different design needs. You can armor a guy head to toe, but then he won't be very mobile unless there's some sort of exoskeleton powered so he can move a lot more weight with more than just his muscles.
If you only protect the vital areas, i.e. chest and back, there's still the shoulder/armpit gap, not to mention the "family jewels", the femoral arteries in the thigh, and other vulnerable spots, and of course, the arms and the head.
So the different "grades" are offered to give people a choice: if you are up against guys with just light pistols light 9mm, then Class II vest should work fine. Level III-A are needed against people armed with 44 Magnums or 45 ACP. If you're up against assault rifles then you will need Level III and Level IV.
Also keep in mind that most cops need vests for both slash protection (against knives and blades) as well as just guns. So for them, Level IIA is probably the best compromise between lightness (so they can wear it every day) and offer general all around protection. Military in general would go for Ievel III or IV due to them seeing more rifles and such.