Robert, there is a separate service record for John Riley Baker's various enlistments in the 32nd Arkansas, the 27th Arkansas, and the 2nd Arkansas (U.S.) Cavalry. The "compiled" part of Compiled Service Records means that, since Civil War soldiers didn't have individual service records, in the modern sense, their service records were compiled after the war from various documents, such as muster rolls, prisoner of war records, receipts for pay and subsistence, hospital records, etc.

As far as pensions are concerned, a veteran could apply for a Confederate pension or a U.S. pension, but not both. For example, one of the requirements for a Confederate pension was proof that the applicant had been honorably separated from the service (discharge, resignation, or surrender at the end of the war). Since Baker had left Confederate service to join the U.S. volunteer service, he could not meet that requirement; however, since he was honorably separated from U.S. service (mustered out of service at the end of the war) he could, and did, qualify for a U.S. pension.