Are there more than one type of gradient? The lecturer is saying


  now the rise over run type gradient varies depending on where we choose our points


according to my knowledge rise over run is the gradient, they are the same. (may be I am wrong, please feel free to identify or fix the bugs)

So, are there more than one types of gradient?

Note: the key is on "type".
There is another type of gradient - and it's in the title of the video!

Derivative. The derivative is a different type of gradient that is NOT rise over run. But rather, a limit of rise over run.
Your instructor is probably saying that for a curve or surface the value of the "rise over run" gradient may be different at different places. The definition doesn't change.

(I haven't watched the video.)