The A and the B were essentially the same, just the A had Damascus barrels and the B had Twist barrels. There was quite a bit of variation in the engraving or etching on the A and B Grades. The text in the Baker Gun Quarterly explains that they have a variety of motifs.
The gun in question is a very early gun as it only has the single pin and a screw in the lockplate. Just a bit into the Baker hammerless they went to a lock with three pins.
No. 38 and 5232.jpg