Both things are going on, but the state represents the citizen in more important ways.
Citizens represent their states in a sort of vague way. When citizens go abroad, for example, they are representing their state by being "ambassadors." The things they do will influence the ways in which the people of the countries that they visit perceive their state. This can have an impact on the international image of their state.
But the state represents the citizen in many more important ways. For example, the state represents us when we are victims of crimes. It uses its police to try to apprehend those who committed the crime. It uses prosecutors to represent "the people" against the person who has allegedly committed the crime.