品管的SQE与采购的供应商管理有什么区别？

Of course both of them can exist.
SQE is Supplier Quality Engineering, it belong to Quality department, the primary jobs of SQE is: 1. Supplier quality system and process qualification; 2. Dispose suppliers' material quality issue; 3. Component Qualification; 4. Push and assist supplier do CIP (Continue Improvement Plan).
Supplier management on Purchasing department is different with SQE, they focus on suppliers' business managment, include materials' price, leadtime, payment, even as a bridge between supplier and customer.