What is the differernce between petrochemical and chemical indusry and how we can differentiate them easily?

The petrochemical industry basically falls under the more general chemical industry. It deals with chemical products extracted from or made with petroleum, like plastics, soap, paints, solvents, lubricants, drugs, fertilizers and so on.

You can differentiate between the industries by the material that is used to derive their products from. If the material used by a company is petroleum, natural gas, coal or more specifically chemicals derived from those resources, then such company is said to be in the petrochemical industry.