State is the institution.
Chapter VI : The social pact
Right away, in place of the particular individuality of each contracting party, this act of association produces a moral and collective body, composed of as many members as the assembly has voices, and which receives from this same act its unity, its common self (moi), its life, and its will. This public person, which is thus formed by the union of all the individual members, used to be called a city, and now is called republic or body politic. When it is passive, it is called by its members State, and sovereign
when it is active, power when it is compared to similar bodies.
With regard to the associates, they take collectively the name of people, and
are called individually citizens, inasmuch as they participate in the sovereign
power, and subjects, inasmuch as they are subjected to the laws of
the State. But these terms are often confused and are mistaken for one
another; it is sufficient to be able to distinguish them when they are used
The multitude, with the "pact" (the contract) become a people. Thus, the contract "gives life" to the collective body : the polis, i.e. the Republic.
When passive, this body politic is called the "State"; when active, it is called the "Sovereign".
This means that the collective body when legislates it acts as the Sovereign and when "operates" according to the laws it is the State.