They are different equations the second being more general than the first.

In we are ignoring the fact that t is a continuous variable and just looking at specific points, , , etc. separted by distance h along the t axis.

In we are retaining the continuity of t- here t could beanynumber. Of course, if we take to be some specific value, then define , , , , , etc. then the second equation becomes the same as the first.