State and local government cover powers not granted to the Federal government.
The state governments are modelled after the Federal government and are separated into three branches (Judicial, Legislative and Executive). Each state has it's own Constitution and it's own Governor, a directly elected official who leads the Executive Branch. However, each state will differ in organisation, number of other directly elected officials and terminology.
Local government generally includes two tiers - counties and municipalities. The organisation and terminology used will again vary based on each State Constitution. In general, local government officials (mayors, council members, etc.) are directly elected by the people.
Counties - county or county equivalent is an administrative or political subdivision of a state that consists of a geographic region with specific boundaries and usually some level of governmental authority. The level of authority differs depending on each State Constitution and historical tradition. The generally provide services to municipalities or cities/towns. Called parishes in Louisiana and boroughs in Alaska.
County equivalent - a term used by the Census Bureau for places that are comparable to counties, but called by different names (e.g. Louisiana parishes, Alaska boroughs, independent cities and the District of Columbia)
Municipalities - organized local governments authorized in state constitutions and statutes, established to provide general government for a defined area, generally corresponding to a population centre. Centres include cities, towns (except in Minnesota and Wisconsin), boroughs (except in Alaska) and villages.
State Constitutions - the governing document of a State Government, comparable to the Constitution. All State Constitutions are longer and more detailed then the main Constitution and will address specific issues/legislation that each state historically considered important. New Constitutions and Amendments can be ratified by each state.
State Government - an institutional unit which exercises power below the Federal Government over a defined geographic territory (or state). Each state is made up of an Executive/Judicial/Legislative Branch, and has their own constitution and directly elected governor. However, each state may include different terminology/processes based on their history and Constitution.
State Governor - responsible for implementing state laws and overseeing the operation of the state executive branch. Terms are for four years (except in New Hampshire and Vermont, which have two year terms). Scope of power, qualifications etc. vary with each state.
State Legislature - All 50 States have legislatures made up of elected representatives, who consider matters brought forth by the governor or introduced by its members to create legislation that becomes law. The legislature also approves a State’s budget and initiates tax legislation and articles of impeachment. All States have a bicameral legislature made up of two chambers: a smaller upper house and a larger lower house (except Nebraska which has one house). The smaller upper house is called the Senate and terms are normally for four years; the lower house is often called the House of Representatives (some call it the Assembly or the House of Delegates) and terms are normally for two years.
Township/towns - A subdivision of a county. Sometimes given governmental or administrative power by a State Constitution, and sometimes only used as geographical designation.