“Basic desert” is the view that a person can deserve praise or blame (and, all else equal, reward or punishment) simply because of what they have done, independent of the social consequences of praising, blaming, rewarding, or punishing them. For example, under this view, an irresponsible employee could deserve a wage cut purely because they performed poorly, even if it would not change their behavior, deter similar behavior by their coworkers, or provide any other benefit.
“Moral realism” is the view that there are objective moral facts (e.g., facts about what actions are right and wrong), regardless of what anyone believes.