Is there a difference between "average rate of change" and "rate of change"

Working on Advanced Functions questions...I believe there is only one formula and that is "Rate of Change = Y2 - Y1 / X2- X1" correct?

Well its actually average rate of change, and instantaneous rate of change.

The formula you have given is average rate of change.
Also referred to as a secant line between TWO

Instantaneous rate of change is in calculus and it is referred to as the derivative. Also referred to a tangent line to a certain ONE point.

Pretty cool stuff

That is in fact the average rate of change. This is because you calculate the rate of change over an entire range of numbers (from X1 to X2). Rate of change (or more precisely instantaneous rate of change) is the rate of change at a *specific* point X, not a whole range of points.

The instantaneous rate of change requires calculus to compute, so you shouldn't worry too much about it for now.

There is a case, by the way, that the two are the same. That happens with linear functions, such as y = ax + b. With such functions the two rates are exactly the same.

And the result of that calculation is an average. A single figure that covers the entire region between x1 and x2.

The actual rate of change at any point between those two may be different than the average. Describing the value as an average is simply making this fact explicit.

average rate of change of Y(x) = (Y2-Y1) / (X2-X1)

rate of change = dY/dx = instantaneous rate of change

just that!