Is their only similarity the fact that they are not xUnit (or more precisely, not based on enumerating specific test cases), or is it deeper than that?

Property-based testing (using QuickCheck, ScalaCheck, etc) seem well-suited to a functional programming style where side-effects are avoided. On the other hand, Design by Contract (as implemented in Eiffel) is more suited to OOP languages: you can express post-conditions about the effects of methods, not just their return values.

But both of them involve testing assertions that are true in general (rather than assertions that should be true for a specific test case). And both can be tested using randomly generated inputs (with QuickCheck this is the only way, whereas with Eiffel I believe it is an optional feature of the AutoTest tool).

Is there an umbrella term to encompass both approaches? Or am I imagining a relationship that doesn't really exist.