They are different but related: "specific" is concerned with scope whereas "granular" is concerned with depth, or level of detail.
Perhaps a good analogy to consider is a calendar. A calendar for 2012 might consist of just the number 2012 and a box (not a very good calendar), a box for each month, or a box for each date. These are different levels of granularity, but none of these are more specific - the scope of each calendar is the same (the whole year).
However if we were to consider a calendar that just dealt with a single month, that would be more specific - the scope has been narrowed. Of course the calendar for the month could go into less detail than the one for the year, so something can be more specific but less granular, and vice versa.
In many situations there is a requirement to make an entity more specific or less specific (more general). The calendar for the year can only be converted into a calendar for a specific month if it is sufficiently granular, i.e. if the year is divided into months in the calendar.