It's the same round fired in .50 caliber machine guns fired in a single shot or semi-automatic "sniper" rifle.
The prototype rifle firing the .50 caliber BMG came into being in WWI as an antitank weapon.
It was developed by the Germans to counter the entry of British tanks onto the battlefield.
This was the 13mm Mauser T-Gewehr, which is technically a .503.
During WWII the Russians introduced the 14.5 mm Soviet PTRD anti-tank rifle firing a 930 grain round with a velocity of 3,230 fps. This is technically a .559 caliber.
The actual .50 caliber sniper rifle as we know it came into being in the 1950's through the modification of the PzB 39 for a .50 BMG barrel and receiver. This rifle saw limited service in VietNam, but it precipitated the development of two anti-personnel weapons - both firing the .50 BMG ammo.
The Marine Corps took the smart route with a bolt action for increased accuracy, and the Army went with a gas operated semi-automatic for increased rate of fire ("spray and pray").
Although no firm data supports the idea, rumor has it that the need of the Afghan rebels for defense against the Soviet Hind helicopters kept our heavy gun development and production alive during the years of that conflict.
You are no doubt familiar with the success of our sniper teams using these weapons in both Desert Storm and the ongoing conflict in Iraq so I won't expound on that issue.
It could be said that the .50 caliber is a military weapon, and that would be correct - so is the .30 caliber.
Outside of it's military uses, the .50 caliber sniper rifle is used by many gun enthusiasts for big game hunting and pure shooting pleasure.
One Mile: 
Here's a Web address you might find useful:
Fifty Caliber Shooter's Institute
One thing I can add:
If you ever shoot one, you'll be hooked for life!