The first definition is better as it defines the institution of government. The second is not so good because a government does more than make laws (the legislative role). It also has executive and judicial roles.
The best definition or, at least, the definition that better expresses what I understand what a government is, is the first option. It says that government is the institution created by a society to create and enforce public policies.
Explanation:
The Government is the main pillar of the State; the authority that directs, controls and administers its institutions, which consists in the general political conduction of the society and the exercise of the executive power of the State.
