In the United States Army, per TO&E 7-17 (Infantry Rifle Company) dated February 26, 1944, the rifle platoon was broken down as follows. On paper, every member of the platoon was issued with an M1 rifle except the platoon leader, the automatic riflemen, and one man per rifle platoon designated as sharpshooter by the platoon leader.
With Change 1 to TO&E 7-17, of June 30, 1944, six M3 submachine guns and six M1918A2 Browning Automatic Rifles were issued unallocated to the company headquarters, for distribution as the company commander saw fit; these often went to squad leaders or to the rifle squads. Keep in mind that soldiers often won't bother to use the weapon that the table of organization says they should use; they'll use whatever they like, and more often, whatever has a better chance of saving their neck.
Platoon Headquarters:
Men:
| Quantity | SSN | Rank | Role |
|---|---|---|---|
| 1c | 1542 | First or Second Lieutenant | Platoon leader |
| 1r | 745 | Technical Sergeant | Platoon sergeant |
| 1gr | 745 | Staff Sergeant | Platoon guide |
| 2r | 745 | Pvt./Pfc. | Messenger |
Equipment:
| Equipment | Quantity |
|---|---|
| Carbine, cal. .30, M1 | 1 |
| Launcher, grenade, M7 | 1 |
| Rifle, U.S., cal. .30, M1 | 4 |
Three Rifle Squads, each:
Men:
| Quantity | SSN | Rank | Role |
|---|---|---|---|
| 1r | 745 | Staff Sergeant | Squad leader |
| 1gr | 745 | Sergeant | Squad leader, assistant |
| 7r(2gr) | 745 | Pvt./Pfc. | Rifleman |
| 1b | 746 | Pvt./Pfc. | Rifleman, automatic |
| 1r | 746 | Pvt./Pfc. | Rifleman, automatic, assistant |
| 1r | 746 | Pvt./Pfc. | Ammunition bearer |
Equipment:
| Equipment | Quantity |
|---|---|
| Launcher, grenade, M7 | 3 |
| Rifle, U.S., cal. .30, M1 | 11 |
| Rifle, Browning, automatic, cal. .30, M1918A2 | 1 |
Equipment for Issue:
| Equipment | Quantity |
|---|---|
| Rifle, U.S., cal. .30, M1903A4 (sniper's) | 1 |
b: Armed with rifle, automatic, cal. .30
c: Armed with carbine, cal. .30
g: Armed with launcher, grenade, M7. Three individuals per rifle squad will be armed with launcher, grenade, M7
r: Armed with rifle, cal. .30, M1, unless otherwise indicated. One individual per rifle platoon, as designated by rifle platoon leader, will be armed with rifle, cal. .30, M1903A4
The following is from "Infantry Training (Volume IV) Tactics: Infantry Section Leading and Platoon Tactics" War Office Code Number 8593, Crown Copyright, by Command of the Army Council, 1950 (Supersedes Infantry Training, Part VIII, 1944)
So, first off, not exactly concurrent with WWII, but it's the oldest pamphlet of its type I have to hand, and by and large nothing had changed altogether with regards to your question from '44 to '50.
First, the establishment of a British (or Commonwealth) Rifle Platoon (pg 13)
Platoon organization
Platoon headquarters Commander (Subaltern) -that is a junior officer; 2Lt or Lt
Sergeant
2-inch mortar NCO IC (In Command)
" " " " No. 1
" " " " No. 2
Orderly (platoon clerk)
Batman (Officer's personal valet)
Each Section
Section Commander (Corporal)
Rifle group- seven riflemen
Bren group- Second IC Section (L/Cpl)
Bren No. 1
Bren No. 2
The corresponding chart indicates that the Platoon and Section Commanders would be armed with a "machine carbine" an SMG in other words, and in this case the Sten SMG; although officers sometimes opted to arm themselves with rifles and adopt subdued uniforms to blend in with the men and not stand themselves out to snipers.
Now, the reason as to why Section Commanders and Platoon Commanders are armed with weapons that really only meant for, as the pam. says "close range work up to 100 yards" is that Commanders are meant to direct the battle, particularly the stages of fire and movement, inclusive of fire orders (target indications, rate of fire) and thus rely on the rifles and Bren gun to deliver effective fire onto the enemy.
As the Section Commander directs the assault- that is, travelling with the riflemen while the Bren team lays down a base of fire, the Sten is used as a means of suppressing fire- no real need to be accurate, but sending enough lead Jerry's way to keep their heads down while the assault team gets close enough to deliver a grenade and follow through with the bayonet.
Hope this helps, let me know if you need any further info.
(The great thing is that, besides the changes in uniform and weapons system, the tactics are essentially the same now as they were then- reading this pamphlet it's clear that I, a former Canadian Army Section Commander, would see very little difference in HOW things are done)
So the two excellent answers already explain the "how" but not the "why", AFAICS. Were SMGs considered better? Or was there something advantageous about them to their role? I'd find this very interesting to know. On a bit of a sillier scale, it certainly used to be that Space Marine squad leaders came with pistols instead of the carbine all the other unit members got, and I've always wondered why.