State has four basic elements: people, territory, government and sovereignty. The absence of any of these elements will not make a state a state. Thus, the state cannot exists without a government. There can be a government however even without there being a state. Government may exist as long as a particular society wanted to continue to have institutions that will carry out the rules of action which are necessary for them to live in a social state.
A state is permanent while a government is not. A government may come and go, it may be overthrown. But the state continues to be unimpaired and unaffected.
A state is an ideal person, intangible, indivisible and immtable. It can do no wrong. The government is an agency of the state. It is perfect if it acts within the sphere. Whatever done wrong is attributed to the government and not to the state.