David, in my opinion the two soldiers being the same are plausible. I did see mention where Captain William H. King was from Marion, Alabama which as you know is in Perry County, Alabama. And Sergeant William H. King was also from Perry County Alabama according to his CMSR's. One would think there would not be that many William H. King's from Perry County Alabama in 1860. However, stranger things have happened and with other soldiers from various counties or even states it is not conclusive these two soldiers were one in the same especially with a common first name and surname. Since some public libraries have ancestry try and see who his parents were and the date of the marriage etc. Sometimes family members know a great deal about their ancestors and your answers may be in their records.