Here is how I would match the examples to the types of public policy:
Regulating businesses: Requiring businesses to meet certain health, safety and environmental standards.
Economic policy: Lowering interest rates to stimulate the economy.
Social policy: Passing legislation to provide paid family leave.
Managing taxes: Reducing income tax rates.
Providing public assistance: Funding programs like Medicaid, food stamps and unemployment benefits.
Funding public schools: Allocating funding from state and local budgets to run public K-12 schools.
Signing trade agreements: Negotiating trade deals with other countries to regulate imports and exports.
Maintaining a military: Funding and overseeing the armed forces through the Department of Defense.
Foreign policy: Promoting diplomatic relations with other countries.
In summary, public policy can generally be categorized as economic, social, regulatory, fiscal (managing taxes and spending), educational, military and foreign policy. The examples given represent actions the government takes within each of those broad types of policy.