They use different plastics because they are produced using different methods. The bottle is produced by injection molding the top part with the threading and blow molding the rest. There are many things that have to be taken into account when choosing the right polymer to use (and price is only one of them). The ability to blow mold, the strength of the plastic (ie the ability to stack several cases of water on top of each other, amounting to potentially thousands of pounds), the flexibility (A bottle with little flexibility could puncture easily. The injection molded lid then has to have different characteristics in order to work properly. Trust me, the makers are not stupid. A water bottle is incredibly complex and it takes enormous amounts of knowledge and experience to create. You need understandings of biology, chemistry, physics, engineering and economics to design that little thing that costs pennies to make.
To summarize: Try and design something that has the following characteristics (which is only a fraction of what is required) then come back and tell me that bottle designers are stupid:
1)Has to contain a liquid without leaking
2)Has to be relatively puncture proof
3)Has to be lightweight
4)Has to be cheap
5)Needs to be manufactured quickly and must be able to be produced by machine perfectly every time.
6)Has to be able to support thousands of pounds while filled with liquid without breaking or deforming (this isn't an exaggeration. Cases of water will be stacked 6 or 7 tall on a pallet then two or three more full pallets will be stacked on top of that.)
7)Has to be ergonomic
8)Has to withstand heat and freezing temperatures and the tendency for the liquid inside to expand when frozen
9)Has to have a unique shape for branding purposes and still meet all the above criteria
10)Needs to be designed to maximize the quantity on a pallet and in turn maximize the quantity on a truck. Most bottles have short necks for this reason (then go and try and create a short neck that is capable of withstanding weight)
11) The lid needs to be able to be removed easily, but still is able to withstand the weight, the pressure and the temperature changes without leaking.