This is a similar question to one that was asked a
couple of months ago.
The A,B,C, and D designations pertain to the diameter of the barrel at the breech. In that sense, they relate to the overall barrel size and its weight. That's why the terms "A weight (wt.)", "B wt.", "C wt.", etc. are used.
An "A wt." barrel generally has a breech diameter of 0.937" or 15/16".
The "B wt." barrel generally has a breech diameter of 1.000".
The "C wt." barrel generally has a breech diameter of 1.062" or 1-1/16".
The "D wt." barrel generally has a breech diameter of 1.125" or 1-1/8".
The profile and length of the barrel will be different depending on the particular barrel pattern, "Lancaster or Dickert", "Golden Age/York", "Jaeger", but the diameter at the breech will be the same for the each letter designation in each pattern.
These barrel profiles have been somewhat standardized among barrel makers so they fit the pre-carved stocks and kits sold by the various suppliers.
There are exceptions when a barrel maker offers a barrel that more closely replicates a historic barrel type rather than the more common generic type.