I'm confused.

You are hung up on the script on the fender. Get over it. The fender script saying it is a "Barracuda" doesn't mean it is not a "cuda". Despite what the script says, any "Barracuda" is a "cuda". Maybe this is an old-timers point of view since we were there in the beginning and younger men only see the fender script.
From 1970 to 1974 , regarding the VINs
Barracudas began with BH, while
'Cudas began with BS, and
Gran Coupes with BP