The additional benefits that open up from a given situation are called by the Department of Veterans Affairs (VA) 'derivative' benefits. To better explain this, and to ease the understanding between a primary benefit and its derivative benefit(s), VA built a Derivative-Benefits Eligibility Matrix. On this webpage, there are three matrices and, depending on which one you click, will lead you to a table where you identify your situation. The three matrices are very basic: Service-Connected, Non-Service Connected and Circumstance.
For more overviews on all veteran benefits, visit the Military.com Benefits Center.