Amit what you understood is almost correct. From my experience, Project Management closes with the final stages of
APQP. In our APQP elements, we had seven gateways which included customer satisfaction. Once the customer accepts the product, the project closes with Project closure steps as specified in Project Closure stage and documenting lessons learned during the entire project.
Then you said in the last line, APQP is for suppliers and Project management is for customer/OEM. In the last line you negated all that was said before.
Please, if you see a project management plan/ Gantt chart you will better understand that APQP elements are activities embedded in the project management plan.
Remember Ford, GM and Chrysler had created the APQP process and PPAP process. All the OEMs still utilize APQP in their product development activities and expect PPAP from the suppliers.
PPAP submission is sufficient for Supplier, hence tracking it with an excel sheet is sufficient. For APQP process spanning a year or so with lot of activities to be completed, its necessary to utilize Project Management with APQP to be more efficient and effective.
What do you think is there in the project management plan? (Just take a moment to ponder on it)
Project management plan has activities that need to be completed, when it needs to be completed, who needs to complete what activity etc.
Please provide feedback, if you understood.