Rule Inheritance is a very broad topic in Pega which is futher discussed in the Senior System Architect course. You can also get more information here: https://docs-previous.pega.com/how-class-inheritance-works.

Pega 7 supports reuse and sharing of rules through a range of features that affect rule resolution. One of these features is Pega's use of Pattern and Directed inheritance.

Basically, the algorithm will search for rules needed to execute by pattern first, once that pattern is exhausted, the search then seeks rule records by Directed Inheritance specified in the class rule itself.

If DemoClass "find by pattern first" is deselected, then direct inheratace is applied from that point in the search and the naming convention would be secondary.

The algorithm is going to find all "potential" candidate. following an order, and execute only that rule  form if DemoClass is not set to "find by pattern first", then the rule resolution algorithm will search the direct pattern parent specified in the DemoClass rule record.

When we want to used Pega Standard functionalities we will inherit Pega Classes using direct inheritance.

Directed inheritance is useful when you want to adopt behaviors that are not available through the pattern chain. Typically, you do this to inherit from the base product, a framework layer, or division layer of the application.

When we want to use our application specific functionalities we will go for pattern inheritance.

Any time you need to specialize common classes, that are reused throughout your application or environment, and you want to subclass them in your own class structure, you'll use directed inheritance.

There is a great ongoing conversation about Pega Inheritance in the Pega Support Community here: https://pdn.pega.com/community/pega-product-support?search=inheritance&sort=relevance