In layman's terms, what is the difference between OpenAthens and Shibboleth?
The Shibboleth Wikipedia page is a good place to start.

Shibboleth is a single sign-on log-in system.... It allows people to sign in using just one identity to various systems run by federations of different organizations or institutions. The federations are often universities or public service organizations.

So, Shibboleth is a software program that large organizations can use to handle having users sign in. It's free software that the organizations can download and use. One nice thing about it is that it supports interoperability: for example, two affiliated universities can form a &quot;federation&quot; within Shibboleth. This allows them to each provide content to their students without sharing content with each other. Better yet, students enrolled at both universities won't need two separate accounts. But, Shibboleth must be set up and maintained by the institutions themselves.
As your link above says, OpenAthens is very similar -- it is more-or-less a large Shibboleth  federation that is managed by a non-profit and comes with a dedicated IT team and help desk. So, a university could just pay to join OpenAthens, and OpenAthens' own employees would help to set everything up, maintain it, and provide user support. Since many institutions use OpenAthens, it is convenient for the end-user as well -- they can use one account for many different content providers, even content providers who don't have any direct relationship with each other.
Note, this is not exclusive to Academia -- large businesses could use this software as well. But in my experience, many people encounter these concepts when dealing with universities or academic publishers.