a flow rule includes items like assignments, connectors, decision shapes, smartshapes, etc., they represent work items, human based or automated and they can have a varying complexity: single step, multistep or refer to another case-type (subcase).
a flow action rule instead has one main function: to point to a section rule to be displayed to the user. The flow action rule is referenced in the connector that goes out of an assignment shape and points to a section.
a flow rule is a process related rule. a flow action rule is UI related.