Objective vs. KPI

In answer to your questions:
1 - The KPI (or Key Performance Indicator) is the measurement that you use to know that a process is performing as expected. For instance, if you are judging an assembly process by how many non-conforming assemblies are made your KPI could be percentage of good product made. This can be tracked to ensure that your process is staying on track, with a goal of perhaps >95% good product. An objective, on the other hand, is an improvement target that you are trying to reach. So for the process above you may be currently getting ~95% good product, but you set an objective to improve the process so that that process give 98% good product.
2 - So, I would say that the statement is almost right. The purpose of the KPI is to track that the process is running as expected, and also provides information that lets you know if your improvement initiatives are being achieved.

For more on quality objectives see this 9100Academy article: https://advisera.com/9100academy/knowledgebase/how-to-define-quality-objectives-in-as9100/
For more on KPIs see this 9001Ac ademy article: https://advisera.com/9001academy/24/define-key-performance-indicators-qms-based-iso-9001/-iso-9001/