The first white man who crossed the Mississippi River and the first white man who crossed the continental divide would probably be two different people. In any case, those are two different events being referred to.
I have never heard of the battle river or the elnoescado.
The continental divide is the part of the North American continent that "divides" the watershed of the countinent. It is located in the Rocky Mountains. The water on one side flows eastward. The water on the other side flows westward.