I'm going off memory here, and it ain't what it used to be, but...
The AL 300 & 301 were similar to the AL1, AL2 & AL3 series guns from the 70s. The gas system was a more picky on what type of shell was used. Some guns operated best with used to be called "High Brass" or full power loads.
The AL302 & 303 had an improved self-compensating gas system to improve cycling a wider range of shells.
The AL390 guns have a further improved the gas system and have a reputation for handling a wide range of shells from soft target loads to full power 3" shells extremely reliably. Early guns have the humpback receiver and later ones have a rounded receiver. There are fans of both types. Both are equally reliable. Available in both wood and plastic furniture.
As mentioned, the AL3901 was a US made version of the AL390 targeting lower cost outlets like Walmart. Plastic furniture instead of wood. I think there is a matt finish on metal. I think the magazine release button was also eliminated but I could be wrong.
The AL391 was Beretta's answer to complaints from some shooters that the AL390's forearm grip was too big or bulky. The gas system was redesigned to fit into a sleeker forearm. Some people prefer it and some prefer the 390 forearm. I think they also introduced 3.5" versions of the 391.
The AL400 is Beretta's current version of a gas operated semi-auto shotgun. I'm not sure what the changes are because I already have an AL390 and an AL391 and I can find no reason to get rid of them for a newer model. If the 400 series is as good as my 390 and 391, it should be a very good gun.
On a related note, Beretta also sold some inertia recoil field guns in the '80s and '90s. The model 1200 and 1201 were pretty much the same as Benelli Black Eagles and Montefeltros. With plastic stocks they were very light weight and great for field carry. Reliable too. They did kick pretty hard since the inertia system did not absorb any recoil and the light weight, so they could be punishing on the target range.