Bryan,
The C14 on your buck tag is the date that the shell of the car (buck) was assembled. In your case this happens to be pretty close to the scheduled build date that's on your door tag C15. This isn't always the case. My car, for instance, has a scheduled build date on the door tag (and build sheet) of 10E (May 10th), while the buck tag has F21 (June 21st). The buck tag date is probably as close as you can get to the actual build date - it might have finished the Trim/Chassis line the next day. No real way to tell.
The sheet metal date codes sometimes don't even help very much. Again, looking at the date codes on the metal surrounding the convertible top lift cylinders on my car I have 4-5-B3 on the left and 4-15-B3 on the right. Other sheet metal seems to be consistent with late April as well. But then I have the buck date of June.... Go figure!?
Dates based upon the VIN's correspond to the "scheduled" date not the "actual" build date. Using the Mustang Production Guide, yours is consistent with C15.