There are two main types of federal grants available to organizations: Entitlement (or formula); and discretionary, also known as competitive.
As the name suggests, entitlement grants are provided to organizations based on a pre-determined formula. For example, a grant for after-school programs might tell grantees they’ll receive $100 per student based on certain eligibility criteria like free and reduced lunch program enrollment. Formula grants most often go to public entities (cities, counties, school districts).
Discretionary grants are awarded to organizations through a competitive application process: Congress appropriates funds; the funding department issues a request for proposals; applicants submit their proposals; a review committee reviews and scores the submissions; and ultimately, grants are awarded to the highest scoring applications.