As pdxyyz said, the only difference is food coloring. The general rule is that cheddars made in the "middle" of the US (like Wisconsin) are colored, while their counterparts on (or near) the coasts (New York, Vermont, Oregon, California) are white. Monterey Jack is the white (California) version of colored colby in Wisconsin. It even extends to processed cheese such as Velveeta and processed American, since the residents are used to the yellow or white color of the natural cheese.
When I was working at the store (in Illinois), we had some customers who were originally from the East (I think New York). They said that the cheese we had just didn’t taste right and asked if I could get white Velveeta for them. It took some doing, but I did get it, and they were very happy.