Line vs interpolation?

Question

What is difference between 'line' and interpolation?

Apparently both are linked such that process of interpolation makes a lines

The following SO question especially its comments created confusion in this regard about difference between a line and interpolation

https://stackoverflow.com/questions/61046619/confusion-understanding-matlab-plot-command?noredirect=1#comment108001784_61046619

Answer 1

Line and interpolation are different things, one is an object, the other is a numerical method.

For your question on stackoverfolw, the plot function is worked based on tracing point method, which means it will draw a segment point by point. For example, if you want to plot a $1$-dimensional continuous function $y= f(x)$, you should give two vectors, one vector contained values of $x$, and the other contained the value of $y$. Then you can seen the curve of your function. The density of data points will affect the smoothness of function. When we given lots of points in the interval, our curve looks like the real continuous function $y = f(x)$.

However, interpolation is a type of estimation, a method of constructing new data points within the range of a discrete set of known data points. You will receive the old data points, then construct a function pass these data points, this function can be linear(two points), quadratic(three points), or more complex functions. Remember your function will exact on these data points.

Indeed, if we had to give relevance between line and interpolation, then I would say MATLAB plot function works like piecewise linear interpolation.