The original Panzer IV had a short barrel howitzer like gun, a 75mm L/24 gun. It was ment for using HE against infantry and fortifactions, similar to M4 Sherman.
The original Panzer III had an anti-tank gun, 37mm L/45 and was ment to destroy enemy armor similar to M10 Wolverine. This may seem like a very weak gun, but remember that this was early in the war and at the time so was the 37mm the standard German AT gun.
Note that the key part of this doctrine was not using anti-tank guns, but that some tanks would use guns unsuited for taking on enemy tanks while the anti-tank ones would protect them.
Germany realised this wasn't an optimal strategy so mostly moved away from it while USA did not until later in the war.
The M3 75 on the Sherman was a dual purpose gun perfectly capable of destroying Pz.III & IV from any angle, and V or VI from the sides or the front within common distances. The 75mm L/24 was half the length of the 75mm M3. They were completely different guns.
An HVAP round was even developed for 75mm M3 but unfortunately not widely produced or supplied. That round would have made an M3 easily capable of dismantling the Pz. V and VI from the front at most combat distances.
Development of the 76mm M1 was pursued instead, which allowed for regular AP rounds to frontally dismantle Panthers and Tigers.
Your understanding of American TD and Armour doctrine is also deficient:
American TD Doctrine was defensive, not offensive. TDs were not intended to 'protect tanks'.
You can read the FMs yourself. American TDs were intended to react to enemy armour breakthroughs and stop breakthroughs.
That would generally be in defense of Infantry, not Tanks.
Many of the American TDs had the same guns as the Tanks, such as the M3 75mm.
They were intended to be fast and cheap, to react to breakthroughs in high numbers, not 'protect' Shermans, which were perfectly capable of protecting themselves.
The whole purpose of American Anti-Tank TD doctrine was to resist encirclement by German armour attempting to 'avoid' engaging American tanks by going around them. This rarely played out in reality as the USA ended up almost entirely on the offensive, making the TD doctrine largely irrelevant.
