I believe Wikipedia is a good reference here, to quote:
Relationship between state and government
Although the terms "state" and "government" are often used interchangeably,[54] international law distinguishes between a non-physical state and its government; and in fact, the concept of "government-in-exile" is predicated upon that distinction.[55] States are non-physical juridical entities, and not organisations of any kind.[56] However, ordinarily, only the government of a state can obligate or bind the state, for example by treaty.[55]
So, an entity capable of binding or obligating associated "states" appears to be a more definitive characterization of a "government".
Unfortunately, usage appears to be less strict and interchangeable as noted by the following comment (same source) on the meaning of the concept of statehood/state in international law per the declarative theory:
the declarative theory of statehood defines a state as a person in international law if it meets the following criteria: 1) a defined territory; 2) a permanent population; 3) a government and 4) a capacity to enter into relations with other states. According to declarative theory, an entity's statehood is independent of its recognition by other states, as long as the sovereignty was not gained by military force. The declarative model was most famously expressed in the 1933 Montevideo Convention.[25]
The above is in contrast to constitutive theory in international law, as outlined as follows:
The constitutive theory of statehood defines a state as a person of international law if, and only if, it is recognised as sovereign by at least one other state. This theory of recognition was developed in the 19th century. Under it, a state was sovereign if another sovereign state recognised it as such. Because of this, new states could not immediately become part of the international community or be bound by international law, and recognised nations did not have to respect international law in their dealings with them.[22] In 1815, at the Congress of Vienna, the Final Act recognised only 39 sovereign states in the European diplomatic system, and as a result, it was firmly established that in the future new states would have to be recognised by other states, and that meant in practice recognition by one or more of the great powers.[23]
So, indeed, a more confusing and complex subject than one might first suspect.