The correct answer to this open question is the following.
Although there are no options attached, we can say the following.
The difference between what Lincoln calls "a government proper" and "an association of states in the nature of a contract merely," is explained in the ideas that were expressed by US President Abraham Lincoln during his inaugural speech of March 4, 1881.
President Lincoln considered that the United States was a Union of those states, formally constituted under the Constitution. That has been the decision and form of government decided by the founding fathers of America.
The country was not based on an association of states in the nature of a contract merely, as some southern states had planned in the case Lincoln won the presidency. Indeed, before the Civil War, some states seceded from the Union and formed the Confederation.
That is why he always insisted on the importance of maintaining the Union. For President Lincoln, the states had decided to create a Constitution to have a more proper and perfect Union.
