Full Idea
What plays the role of sense is not information in a file, but the file itself. If there are two distinct files, one for 'Cicero' and one for 'Tully', then there are two distinct (non-descriptive) senses, even if the information in both files is the same.
Clarification
Cicero and Tully were the same person
Gist of Idea
Sense is a mental file (not its contents); similar files for Cicero and Tully are two senses
Source
François Recanati (Mental Files [2012], 3.4)
Book Reference
Recanati,François: 'Mental Files' [OUP 2012], p.41
A Reaction
This may be the best idea in Recanati's book. A sense might be a 'way of coming at the information', rather than some set of descriptions.
Related Idea
Idea 16360 Identity statements are informative if they link separate mental files [Recanati]