Rusty and Cobalt, the Thompson SMG pictured is an M1A1. This was the most common and differed from the Model 1928 because it was a simpler design, eliminated the Blish delay lock, did not have a detachable rear stock, nor a ribbed barrel. The M1A1 also didn't take a compensator, only had a horizontal front stock/grip, a simple rear leaf sight and could not be fitted for the 50 or 100 rd drum. It took a 20 or 30 rd stick mag. The Model 1927 was rarer than eyeteeth, but the Model 1928A-1 was developed as a military issue with the addition of sling swivels and sometimes a different compensator other than the CUTTS. The bolt cocking handle (on top of the receiver) was beefier than the civilian/police model '28. There's a lot more variations involving blued vs. Parkerized finishes, but them there is the basics. Hope it helped. ps. they were both a blast to fire on full auto
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JP