What is the difference between Domain Error Testing and Control-Flow/Data-flow testing?

I can currently read the following explanation:

There is a fundamental difference between flow graph–based testing techniques and domain testing. By flow graph we mean control flow graph and data flow graph. The difference is explained as follows: Select paths from a control flow graph or a data flow graph to satisfy certain coverage criteria. To remind the reader, the control flow coverage criteria are statement coverage, branch coverage, and predicate coverage. Similarly, the criteria studied to cover the definition and use aspects of variables in a program are all-defs, all-c-uses, all-p-uses, and all-uses, to name a few. The path predicates were analyzed to derive test data. While selecting paths and the corresponding test data, no assumption is made regarding the actual type of faults that the selected test cases could potentially uncover, that is, no specific types of faults are explicitly considered for detection.

Domain error testing takes an entirely new approach to fault detection. One defines a category of faults, called domain errors, and selects test data to detect those faults. If a program has domain errors, those will be revealed by the test cases.

It's still not quite clear to me what is the key difference between domain error testing and control-flow/data-flow testing? And what are the advantages of domain error testing over control-flow/data-flow testing?