Interpolation versus Curve Fitting

Given a set of data
$y_i=f(x_i)~~~~~~i=1,\ldots,n$
obtained from an experiment or from some calculation.
In curve fitting, the approximating function passes near the data points, but (usually) not exactly through them. There is some uncertainty in the data.
In interpolation, process inherently assumes that the data have no uncertainty. The interpolation function passes exactly through each of the known data points.

Figure shows a plot of some hypothetical experimental data, a curve fit function and interpolating with piecewise-linear function.