In Florida we call them "nucellar" or "old line." The idea is that an old-line cultivar has been budded from an old tree, without going through the nucellar seedling process. The advantage is that it will not show juvenile characteristics (upright growth, thorniness, lack of fruit or fruit mostly in the top of the tree). The downside is that it may carry one or more virus or viroid diseases. Nucellars are virtually always free of such diseases, since most viruses don't pass to the seed. But then it takes a while to get rid of the juvenile characteristics of such seedlings. I presume that's what is going on here.
