I believe this is actually an example of what's known as a "proportional derivative controller", which is effectively an underdamped spring. With a PD controller, the further the target points are apart, the faster the interpolation.

Lerp, on the other hand, is linear; the interpolation speed should not change:

Lerp(int A, int B, float t) { return (1.f-t)A + (tB); }

In the example implementation I present, it's assumed that t is pre-modulated by the framerate delta time, and within the bounds (0.f, 1.f)

You can easily make a PD controller out of a lerp, but (without a lot of gymnastics) you can't create a lerp out of a PDC.. at least as far as I know.