Grants are how the federal government provides aid to states. There are two types.
Categorical grants are the main source of aid to state and local governments. They may be only used for one specific category of state and local spending. Instead of directly ordering states to do things, most grants come with special conditions. So, these grants come with strings attached, and the most common string is a nondiscrimination provision, meaning the aid can't be used for purposes that discriminate against anyone. Another common string is that funds can't support construction projects that pay below the minimum wage.
Crossover sanctions mean using federal dollars in one program to influence state and local policy in another. For example, funds are withheld for highway construction unless states establish highway beautification programs.
Crosscutting requirements are conditions that if broken, stop all other funds. For example, if a university discriminates in their football team, it would lose funding for all of its programs.
There are two types of categorical grants.
A project grant is given bon the basis of competitive applications. For example, the National Science Foundations grants are examples of project grants.
A formula grant is based on a formula taking into account population, per capita income, percentage of urban population, or other factors. The most common formula grants are for Medicaid, child nutrition programs, and public housing.
Categorical grants are a hassle to get; they require boxes of paperwork, and they only give funding to a very specific topic. Block grants are different. First adopted in 1966, they are given automatically to states, and they are able to spend the money in broad areas such as social services and community development.