For a full explanation of severance pay from the military versus compensation from the VA, please refer to 38 U.S.C., 3.700.3 for the legislative rules governing these differences.
A quick explanation of how VA compensation versus severance disability works is this:
Disability severance pay from the military is granted for a disability received or acquired while in the military and is usually paid in a lump sum. VA compensation is unlike severance pay because it is not paid in a single lump sum, but is paid out over time. If the VA were to pay you compensation and severance pay for the same disability, you would be getting paid twice for the same disability. According to law, this is not allowed.
If you filed for other disabilities that were not related to your disability severance, the VA could possibly pay you for those disabilities.
For all current information about compensation and pension benefits and requirements, etc., go to http://www.vba.va.gov/VBA/ and click on the applicable links.