FWIW
From
TM 9-1904, Ammunition Inspection Guide (1944): "The model number marked on the projectile may be either M51, M51B1 or M51B2 ; rounds so marked are identical in functioning, the B1 or B2 designations signifying only that the projectiles are manufacturing alternatives of the M51."
(from my notes)
M51 (no suffix) design had the ballistic cap (windscreen) crimped on the piercing cap. In service the windscreen had problems with occasionally separating from the projectile before it was supposed to - including in the barrel. It was thought that this occurred partly due to the light construction of, and poor crimping of, the windscreen - and partly due to damage during transit and handling in the field.
M51B1 & B2 designs had a stronger drawn and machined ballistic cap which screwed onto the piercing cap. The piercing caps were of a slightly different shape in order to allow for the screw threads for the ballistic cap.
I think I remember reading that the piercing cap of the B1 was joined to the core differently than on the B2 (one was soldered on?, and one sintered?), but I am not sure.
M51A1 was a training projectile with the core & piercing cap made in one piece from mild steel, without the ballistic cap of the standard M51 service round.
M51A2 was a training projectile with the core, piercing cap, & ballistic cap, all machined as one piece from mild steel, having the same ballistic shape as for the M51/B1/B2 projectiles.