The verb 'procure' means to obtain something with great care, it can be used in a wider context than 'purchase' which is used to refer to something acquired by buying it. In a legal context 'procure' can also be used with the meaning of persuading or causing somebody to do something.
“Procurement” is the overarching function that describes the activities and processes to acquire goods and services. It involves the activities involved in establishing fundamental requirements, sourcing activities such as market research and vendor evaluation and negotiation of contracts. It can also include the purchasing activities required to order and receive goods.
On the other hand, the term “Purchasing” refers to the process of ordering and receiving goods and services. It is a subset of the wider procurement process. Generally, purchasing refers to the process involved in ordering goods such as request, approval, creation of a purchase order record (a Purchase Order or P.O.) and the receipting of goods.