The difference between Rules and Description Logics is that Rules are considered to be applied only on known Constants, which means there is no possibility to create new things on the fly which is possible for example in Description Logics when one uses Existential Quantification.
For example one can say a Human is everybody how has Human Parents which is recursive, and for the human one can insert there exists somebody who has human parents, etc. So one can create on the flight new Instances/Individuals here. This is possible because of the Existential Quantification. This is something one can not do with Rules, because there one has usually not the Existential Quantification.
On the other hand if Rules are considered as First Order Formulas, then the consequence is when one combine these Rules with decidable Description Logic like for example ALC then the combination of both leads to undecidability.
No possibility to "create" new things "on the flight" by using existential quantification ∃
Human ⊑ ∃hasParent.Human