The key difference is in how the two thread into the bottom bracket shell. Like pedals, one side of a BSA standard bottom bracket shell is reverse (left) threaded, while both sides of an Italian standard bottom bracket shell are regularly (right) threaded.
The size of the shell is also different, with BSA bottom brackets using a 1.375” (34.92mm) diameter shell and Italian BB’s using a 36mm diameter shell.
The width of the bottom bracket shell is also different; BSA bottom brackets are usually 68mm or 73mm wide, while Italian threaded bottom brackets come in at 70mm wide.
Both standards use a 24tpi pitch thread.
It’s very rare to encounter an Italian threaded bottom bracket these days as they’re prone to suffering from a phenomenon called precession. Precession occurs when the forces acting on the driver side of the bottom bracket — which is right-hand threaded — make it unscrew from the bottom bracket shell.
BSA bottom brackets are reverse threaded on the drive side to counteract this.
Wheels Manufacturing make an English standard bottom bracket for your road and mountain bike frames.