Please find below explanation for both functionalities :
Save As : Use the Save As form to copy an existing record's functionality to a new record with unique key parts. This form is pre-populated with the original record's key parts and creates default values for the new record's context.
specialized or circumstance rule : You can create a specialized or circumstance rule to create a variant of the rule that can be triggered only conditionally. The created rule is resolved and active only when the specified conditions are met. Create specialized or circumstance rules to address dynamic business requirements without changing the core logic every time.
FYI , Please see the below links for detail explanation :
Thank you for the reply. Your links helped me understand more about circumstancing a rule.
However, I am still not fully understanding "specialize by class or ruleset". It seems that "Save As" already allows you to specialize a rule by class or ruleset, so I can't understand why the "specialize by class or ruleset" feature is necessary.
When I open a rule and click "Save As", I am able to change the Apply To field (Specialize by class) and change the Add to ruleset field (Specialize by ruleset). But, for each rule, there are options for "Save As", "Specialize by class or ruleset", and "Specialize by circumstance" (See attachment).