The "Tommy Gun", or the Thompson model from the 1930's, had a drum magazine and had a version with one handle in the back, and a version with two handles, one in back and one in front.
The Thompson (same gun) from the 1940's was used during World War II, and had a stick magazine, with only a handle in the back. However, there was also a hand guard on the bottom of the barrel, the point was to use that as your "second handle".
There is no real difference between the guns. They are the same. There are various versions, so just chill. Wikipedia the gun before you say "IZ SUPOZD 2 HAV STIK MAGZNE N00BZ".