More common in general engineering is MSN for Manufacturers Serial Number
I think there is a different interpretation between MSN and C/N, though the MSN is incorporated within the C/N. I'll use the P-51 as an example.
The aircraft was produced under the following North American factory identities - NA-73, 83, 91, 97, 99, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 122, 124, 126. Missing numbers were either P-51 projects cancelled or other NA non P-51 projects.
The P-51D was produced as NA-106, 109, 110, 111, 112, 122, 124. 107, 127 and 138 were cancelled or transferred projects, 107 was cancelled and transferred to 103 for production as a C model.
A constructors number (C/N) for a particular P-51D in its entirety thus might be NA-122-30972, the 30972 being the serial number. Four thousand NA-122 aircraft were built.