I am looking for an explanation for the terminology "artificial smoothing" and "artificial diffusion" in the context of numerical schemes.
For instance, consider the upwind scheme where we estimate a derivative of $f$ at $x$ by $$ \frac{f(x)-f(x-h)}{h} $$ where $h>0$ is our mesh-size. This scheme is said to create artificial smoothing. On the other hand, the central discretization $$ \frac{f(x+h)-f(x-h)}{h^2} $$ is said to create artifical diffusion.
How do these concepts explain, for instance, that the upwind discretization is more "stable" in $h$ for problems such as $$ \begin{cases} -\epsilon u^{\prime\prime} + u^\prime =1 &\text{in }(0,1)\\ u(0) = u(1) = 0. \end{cases} $$ when $\epsilon>0$ is small?