'C' series tractor predated 'D' series tractors. Many componets are similar or the same. If the letter 'C' follows a 'C' or a 'D' it does mean the narrow front end. The second letter in a name commonly denotes the specific package the tractor was purchased with, some common ones are below:
'DC', 'DC-3' = Row crop, narrow Front (or adjustable wide front)
'DC-4' = Row Crow, non adjustable wide front
'D' = Standard Tread
'DO' = Orchard model (low profile version of a 'D')
'DV' = Narrow version of a 'DO'
'DI' = Industrial model (heavy duty version of a 'D'
'DE' = Power unit only