Basically you have it correct. Medium varies depending on who's barrel. Anywhere from a consistant 0.75" for the entire barrel, up to a .8something (SPR type). Heavys are in the .95 to 1" range to the FS then 0.75" after.
Bull Barrels are 1" the entire length (chamber to muzzle).
M4 would be a 'Govt Profile" as that is what the Govt uses, and it fits the bill. It just adds a notch for the M203.