I always thought things like plastics, synthetics, pharmacuticals, etc. contained had oil derivatives.

Yes, but it's a very small portion of each barrel.  "Petrochemical feedstocks" account for 1.1 gallons per barrel, according to the American Petroleum Institute.

So a feedstock, like the Naphtha Petro Feed or Oth Oils Petro Feed above, are used as inputs for manufacturing? Sorry, I am not an engineer, so this is all new to me.
As I understand it, yes.  

The API produces this brochure about what is made from oil, for classroom use:

http://www.classroom-energy.org/teachers/oilfacts.pdf

Thanks for the link.