How do you differentiate between procurement and Purchasing and Supply?

The three terms are used synonymously, and also carries overlap in their definition. However, from academic point of view, each one of these three implies separate set of activities. 

Procurement has strategic role i.e Sourcing, Contract Mnagement, negotiating pricing and terms of the contract, etc etc.Purchasing refers to operational side i.e the actual act of buying.

Procurement - Organizational function that includes specifications development, value analysis, supplier market research, negotiation, buying activities, contract administration, inventory control, traffic, receiving and stores. Purchasing - A major function of an organization that is responsible for acquisition of required materials, services and equipment.

Supply chain is a process of optimizing the flow of material, information and funds within and among organizations.

Purchasing decisions are what to buy, where to buy, and how much to buy.

Procurement has additional responsibilities, how much to pay, when to pay and how to pay.

The supply chain consists of everybody involved in getting the product in the hands of a customer. (supplier, payment, warehouse, transportation, logitics,  etc.) The supply chain can be considered the entire chair, while procurement is a part of the chair.