Question

what is the different between dy and delta-y?

Answer 1

An easy way to think about it is:
\[\Delta y\] is a finite difference that you can measure.
\[dy\] is an infinitely small difference.

Answer 2

dy is a derivative and delta y is a change in y

Answer 3

Also, as mykal pointed out, you can think of them in terms of functions as in the following diagram. Imagine that as Delta-x becomes smaller and smaller, Delta-y becomes dy.