The five weapons you've listed span 4 firearms categories.

The M1 is a full sized rifle. It is intended to engage targets up to several hundred meters away with reasonable accuracy. It has a low magazine size, with relatively low rate of fire, but each shot is relatively powerful.

The Thompson and Grease guns are submachineguns. They are intended to engage targets at close range (really up to around a hundred meters). They have relatively large magazine sizes, with high rate of fire, and relatively weaker ammo. However, because of their weaker ammo, they have reduced recoil, which is what makes them practical to use as a shoulder fired automatic weapon. The Grease Gun was intended to be a replacement for the Thompson, which is relatively heavy and expensive and difficult to manufacture, especially when compared to the submachineguns fielded by the other major armies of WW2.

The BAR is an automatic rifle/light machine gun. It fires the same cartridge as the M1, but from a larger magazine and is capable of automatic fire. The BAR was developed during WW1 to implement a strategy called walking fire, but was used as a light machine gun during WW2. The BAR is significantly heavier and bulkier than the M1.

The M1 Carbine is a bit weird. It's a lightweight (originally) semiautomatic weapon firing this weird intermediate cartridge. It was originally designed as a smaller, cheaper, lighter weapon for non-infantry men, but was pressed into use for various infantrymen (especially paratrooper) roles (because of its lightness).

Now, within the context of WW2, this mix of weapons isn't that bizarre - really the only weapon/category that isn't clearly mirrored in other armies is the M1 carbine.

Perhaps the missing piece to your question (especially in comparison with today's US Army equipment) is the absence of an assault rifle. Today's infantry forces are predominately equipped with an assualt rifle (or carbine variant) and directly supported at the fireteam level with a light machine gun of some sort. The assault rifle as a concept bridged the gap between the full sized rifle (the M1 Garand in USA WW2 terms) and submachingunes. The intermediate cartridges used in assault rifles permit the individual soldier to effectively engage targets from close range out to a few hundred meters. The reduced recoil of the cartridges permit the use of automatic fire, while the increased bullet velocity makes aiming out to distance an easier task.

The assault rifle as a concept did not exist prior to WW2 - it was effectively invented/popularized by the StG-44 during WW2.