Short answers, pulled from the story.
The Panzer III was designed to fight other armored vehicles in direct combat, firing armor-piercing shells at enemy tanks. It was intended as the primary battle tank of German Panzer divisions, paired with the Panzer IV, which handled infantry support and anti-tank gun positions.
The Panzer III's main gun, limited by the physical dimensions of its turret ring, could not be upgraded beyond a 50 mm caliber. The T-34 and KV-1 tanks carried heavier armor and required more powerful weapons than the turret ring could accommodate. The Panzer IV, with a larger turret ring, was redesigned to mount the long-barrelled 7.5 cm KwK 40 and took over as Germany's main medium tank.
About 18,000 vehicles based on the Panzer III chassis were produced across all variants, more than any other German armored fighting vehicle design of the war. This total accounted for over a quarter of all tanks and assault guns built by Nazi Germany.
The Panzer III served with Erwin Rommel's Afrika Korps from early 1941, mostly equipped with the 50 mm KwK 38 L/42 gun. It performed well against British Crusader and American M3 Stuart light tanks but was outmatched by the heavily armored Matilda II infantry tank and the M3 Lee/Grant medium tank, whose 75 mm hull gun could destroy a Panzer III beyond its own effective range.
The Panzer IV and the Panzer V Panther replaced the Panzer III after the German defeat at the Battle of Kursk in the summer of 1943. The Panzer III was relegated to secondary roles including tank training and reconnaissance.
The most significant was the Sturmgeschütz III assault gun, which became the single most-produced German armored fighting vehicle of World War II. Other derivatives included the Flammpanzer III flamethrower tank (100 built), the Sturmhaubitze 42 assault howitzer (1,299 built by Alkett between March 1943 and 1945), and the Sturm-Infanteriegeschütz 33B heavy assault gun (24 built, 12 lost at Stalingrad). The Soviet SU-76i assault gun was also built from approximately 201 captured Panzer III and StuG III hulls at Factory No. 37 in Sverdlovsk in 1943.