You have to have registered for a Distinguished Degree when you first enroll into University. Each University will specialise in certain facets, and you can tell if these are distinguishable by the bronze marker, or medal, next to the thumbnail for the degree.
Depending on the level of your sims skills at the time of their application they may have not had high enough skills to get them into a distinguishable degree. Most of my sims that have had gone to study a Distinguished Degree have usually had level 7+ in the skill that related to that degree.
Hope that helps, but well done on getting honours, your Sim must have worked really hard to get it! ?