Tom Hanks famously depicted Captain John Miller in “Saving Private Ryan” toting his trusty Thompson submachine gun — “Tommy gun” — from the beaches of Normandy far into the interior of France in 1944.

The Thompson submachine gun and the M3 submachine gun, two classic submachine guns (SMGs), helped American GIs win World War II. Both fired the same powerful and ever-beloved .45 ACP (Automatic Colt ...