Purchasing is a component of SAP MM module and its process can be roughly depicted in below diagram.
MRP (material resource planning) creates procurement proposal and later gets converted into Purchase Requisition. Next step is assigning source to Purchase Requisition, and release of Purchase Requisition. The PR gets converted to Purchase Order and upon goods receipt an invoice receipt can be done to complete the purchasing process. Additionally payment is processed (in FI module).
Procurement doesn’t have to start by the MRP, it can be initiated by consumption based planning or by direct creation of PR or PO.
MRP is a system function to determine the material requirements on both the material and BoM level. A BoM (Bill of Materials) is a list of components and subcomponents a single material is consisting of.