A government is the body that runs a state. A government consists of a prime minister and some politicians (or governors). Each government is split into many departments, which decide what is best for them, their citizens and their state. Governments make rules, deciding what can and cannot take place in their state.
The State is the area controlled by a particular government, usually the same area as is called the country. The state includes all the businesses, politicians and citizens within it.
A politician is someone – usually working for the government – who participates in politics. Politicians are a main part of the government; advising the prime minister on good solutions and ideas to sort problems and keep their citizens happy.
A citizen of a state is a person who lives there legally. People who don’t have legal permission to be in a state (eg illegal immigrants) are not considered citizens and can be made to leave.