What is the difference in procedures between PMO procedures and Quality assurance procedures?

Shouldn't be a difference of one aim

We need to understand the meaning of PMO and QA before looking into the procedural differences.

PMO defines and maintains standards for project management within the organization and the primary goal is to achieve benefits from standardizing and following project management processes, policies and methods.

QA is the process of verifying whether a product meets required specifications and customer expectations.

Looking above the definitions they are different in their goals and objectives and thereby the procedures for the same would be different.

PMO procedures focusing in how we manage and control projects in organization and it including some quality assurance to make sure the project managers are follow the standards 

In some Organizations they have a quality department to control the quality  in all organization department and make sure they follow the standards.