There is a general presupposition that someone or something fits the description. The difference between the referential and the attributive use is not a difference in the speaker's beliefs. Propositions are abstract objects representing truth-conditions.
Pragmatics is the study of linguistic acts and the context in which they are performed.
This will, in turn, determine which proposition has been expressed by a given sentence. This, in turn, together with a possible world, determines a truth-value.