Ignition Override,
The 7.62mm bullet is exactly 0.30 inches in diameter as are the American .30-30, .308 and the British .303 bullets. The second and third digits of the latter two calibers serve to indicate the size of the lands in the barrel of the weapons that fire them - an even number of .004" in the former and an odd number of .003" in the latter. The current 7.62 mm NATO is in fact exactly the same round as .308 Winchester.
A 20mm cannon shell is somewhat less than one inch as there are 25.4mm to the inch.
A .50 calibre bullet is not only thicker but also one third longer than a .303/.308 giving it 3.7 times the mass of the smaller bullet.
Moving up to 20mm cannon takes the projectile mass up to five times that of the .50 bullet and almost eighteen times the mass of the .303 bullet. It is easy to see why the larger calibre weapons were preferred by the fighter piots and air gunners. Typical engagement ranges were no more than 150 yards in most cases, its the weight of fire that counts rather than the ballistics.
The best indicator of hits is the bits of metal flying off the enemy aircraft...
...and size really does matter!!