They're not quite the same when it comes to physics, where you have the additional characteristic of precision for theories. For a trivial example, "anything can happen anywhere at any time" certainly covers all observations and is simpler, but has no precision in what it forbids.

Any new theory in physics must have at least the same precision as the known theories. The problem in current physics-at-the-edge (raised by the article) is that these newer theories are coming up with so many ways in which universes can be formed that even though we're moving in the "simpler" direction by relinquishing fundamental some assumptions, we're losing "precision" in this sense. This is now happening to the extent that the very notion that the job of a scientific theory is to only explain the observable universe is being called into question and theories that consider our universe to be just one of many universes with different parameters are also included in the play. At that point, the working assumption that all these universes that our mathematics invents actually exist though we cannot observe them, is a simpler view of the cosmos ... until we know better. However, the practical utility of such an expansive theory ends up being limited relative to the theory that it is trying to replace, since our ability to predict things in our universe is not being improved on.

edit: What I'm trying to say is, I guess, that "precision" and "simplicity" are opposing forces that keep a check on overfitting.