They names of these geographies and how they are related if fairly confusing because they are so similar so I will start by naming all of the players:

Metropolitan Statistical Areas (MSAs) pre2004

Primary Metropolitan Statistical Areas (PMSAs) pre2004

Consolidated Metropolitan Statistical Areas (CMSAs) pre2004

CoreBased Statistical Areas (CBSAs) May 2004 onward

Micropolitan Statistical Areas May 2004 onward (They didn’t give this one an acronym, probably because there were none left. They also stopped using the acronym “MSA” at this time and just referred to Metropolitan Statistical Areas, so I will do the same when talking about the new identification system here as well)
The first 3, MSAs, PMSAs, and CMSAs represent the old Metropolitan Area identification system (pre2004), where PMSAs nest within CMSAs while MSAs are free standing (see the MSACMSZ comparability tab.
CoreBased Statistical Areas (CBSAs) are the newer identification system units and can represent either Metropolitan Statistical Areas or Micropolitan Statistical Areas. However, since no Micropolitan Statistical Area is large enough to be identifiable in the CPS, only Metropolitan Statistical Areas are identified by METAREA and CBSASZ, (you will notice the CBSASZ bins start at “100,00249,999” population). Hopefully this address the first part of your question, but let me know if it does not.
To the second part of your question:
Not quite, is the answer. Every METAREA has an associated size value for CBSASZ in May 2004 onward samples, but for the earlier samples it depends on whether or not an area is an identifiable PMSA nested within an identified CMSA. If the PMSA is identifiable individuals living within it will have independent values for both MSACMSZ (size of the larger CMSA) and MSAPMSZ (size of the specific PMSA within the CMSA), otherwise they should have the same value for both. Everyone with a size value will be identified to a speific METAREA.
I hope this helps.