"Slope" implies that the denominator is a distance. In the context of a graph on paper or screen, it is clear how rise and run are mapped to distances. It's a totally sensible definition: slope only makes sense given a choice of axes.

"Rate" implies that the denominator is a timespan. This does not make sense, as there are many slopes which are not rates and which are not presented as rates.

It's kind of a silly thing to worry about, but Khan's answer is unequivocally better.