It works then just as it does now, enlisting means I sign on to serve, mustering is when I physically appeared and started my service. Many enlisted as proof of loyalty to whichever side was the most powerful in the neighborhood at the time. Often they were never called up to serve or if they were, they didn't show up at the appointed place and time.
Here is your man's listing in Missouri SOS files I think, note date and place scratch throughs.
http://www.sos.mo.gov/Images/Archives/Military/s00859/s00859_0259.pdf
John R