The shotgun pictured being held by Bonnie is a Remington Model 11 (also sold by FN as the Browning Auto 5) in 20 gauge, and had been sawn off front and rear. It can be seen clearly here:
^^You can also see a pair of the sawn-off Browning BARs the gang favoured. Supposedly Clyde also produced a high-capacity magazine by welding together three 20 round mags but I've never seen a picture and that doesn't seem like it would work. There were factory 40 round mags made
for the Polish though, and 30 rounders
for the Swedes.
Clyde used a slightly longer Remington Model 11 in 12 gauge (full stock, ~16" barrel) as well as a Winchester 1887 lever action shotgun in 10 gauge with a sawn off barrel, and a Stevens 520 pump action in 12 gauge sawn off at both ends.
I've never heard of them using Thompsons, nor seen pictures of them with Thomspons. The same goes for a Winchester 1897 (the pump action shotgun pictured on the green back ground and described as a 'converted rifle').
Other weapons used by the Barrow gang include a Krag rifle in .30-40 Krag, a variety of Colt and Smith revolvers and autos, and a Winchester 1907 in .351 Winchester (although there were versions with 16 round magazines produced for soldiers in World War One, and the Dillinger gang
had modified theirs with compensators, vertical grips, and full-auto capability, the Barrow gang used a standard 1907 five round model).
Guns used to kill the pair included a
Colt Monitor in .30-06 (Browning BAR variant designed to be fired off-hand) and a Remington Model 8 in .35 Remington. The latter is often believed to have been the
Model 81 Special Police with the extended 15 round magazine (also produced
with a vertical grip) but this wasn't introduced until a year after the final shoot-out and footage taken of the posse before the shootout shows Hamer with a standard Model 8.