Difference between measurement objectives and process performance objectives

CMMI uses following terms while talking about measurements:

1. Identified information needs and objectives at organization level (MA)
2. Measurement objectives derived from such information needs and objectives (MA/SP 1.1)
3. Quality and Process Performance Objectives (OPP/SG1)

I want to investigate finer differences between the later two. Are they more or less the same? If not, what are the finer differences?

Your first two questions deal with Measurement and Analysis (MA) which is a Maturity Level 2 Process Area (PA). Your third question is about OPP which is a Maturity Level 4 PA.
MA is a support PA that applies to ALL PAs in the CMMI. Its focus is defining measures and indicators that help answer or address a specific information need. An information need can be articulated using the following format:

<someone> needs to know <what information> in order to make <what decision>.

For example, an issue facing the Project Manager may be that Project Plans are inaccurate causing project teams to routinely miss milestones and deliveries.
Therefore the information need would be: The Project Manager needs to evaluate the schedule, progress, and dependencies of key development activities and events in order to determine necessary corrective actions.
Then the measurement concept or strategy for addressing this information need would be: At the end of each week the Project Manager collects estimates to complete the work for each current task and enters the data into the schedule. The Project Manager and team review progress to determine the necessary corrective actions and modify the Project Plan as needed each Monday morning.
Now it becomes very easy to determine the base and derived measures that support the measurement concept.

So these concepts (information need, measurement concept, and measures) are interrelated concepts that help define what data to collect and analyze to help answer a question.

The Quality and Process Performance Objectives (QPPOs) are entirely different from the measurement concept. The QPPOs are objectives set by the organization based on the organization’s business objectives, past performance of projects, and are constrained by the inherent variability or natural bounds of the process. Now, in order to determine the measures that the organization will use to support the QPPOs, the organization should follow the MA process of articulating the information need, defining the measurement concept, and determining the measures.