A preferential entailment is defined by a binary relation, or «preference relation». This relation may be among interpretations, or sets of interpretations, or among «states» which are «copies» of interpretations or of sets of interpretations. This provides four kinds of preferential entailments. The paper deals mainly with propositional logic, however it describes also the situation in first order logic. For instance, the third notion presented above can be seen as a way to simulate the main aspects of the simplest first notion when it is defined in the predicate calculus, while staying in the propositional calculus. Indeed, the third notion allows as many copies of interpretations as we want for a complete theory, even in the propositional calculus, and this is precisely what happens in the predicate calculus. What we do here is to provide a characterization result for these four kinds of preferential entailments. We choose properties as simple and natural as possible, and sometimes we provide various characterizations for the same notion. It appears that the apparently most complicated notion possesses by far the simplest characterization result. A by-product of our results is that the fourth notion is equivalent to the second notion: we may define directly the relation among sets of interpretations, eliminating the need for «states» in this case.