The 20x102 (20 Vulcan) is a descendant of the .60 caliber cartridge. The .60 was an attempt to improved the ballistics, particularly air-air, of the .50 caliber, while also developing an Antitank cartridge. The .50 wasn’t fast enough, didn’t carry enough payload for air to air engagements which were now involving fast jets. The .60 was developed and had some small success, but was quickly necked up to take a 20mm projectile, for even more payload, which we know today as the 20x102. The .60 case was essentially the same as the 20 Vulcan, except for bullet diameter. The US Navy, in the 1980’s did some experimentation at China Lake with the 20 Vulcan case necked to .50 caliber.
As mentioned the 20x110 case was also necked, during WW2, to take a .50 and was known as the .50 HV project.
And, also in the late 40’s/early 50’s, the 60 case was necked down to take the .50 bullet. Several projectile variations were tried.