The standard issue submachine gun for the United States of the Second World War, and by far the most famous, was the Thompson submachine gun. The M1928, M1, and M1A1 were the specific variants that were issued. The Thompson was indeed an excellent weapon, but it was also very heavy for a submachine gun and on top of that it was expensive to produce. To remedy this, in 1944 the United States military adopted a new submachine gun called the M3 Grease Gun.
The M3 Grease Gun may not have been as visually appealing as the Thompson, but it was indeed cheaper to produce by a long shot. It was issued in large quantities at the end of the war, and continued to be issued to the United States military up until the 1990s, when it was still being used by tank crews.