I'm not comparing apples to oranges. I'm comparing apples (brandy) to apples (jack). Apple brandy is featured in drinks such as the Honeymoon, applejack is featured in drinks such as the Jersey Girl, or you could use either one in drinks such as the Jack Rose and the Diamondback. As I've mentioned in others posts, even though they both come from fermented apple cider, the two are similar but not the same.
So what's the difference? Traditionally it's a matter of hot and cold. Apple brandy uses the regular distilling process. This involves heating the cider so that the alcohol evaporates, capturing the vapor, and cooling the vapor so it becomes a liquid again. Applejack involves freezing the cider and siphoning off the liquid alcohol after the water freezes. Both processes separate the alcohol from the water by exploiting their different boiling or freezing points.
Why use the word "traditionally?" Because there's a problem with the old way of making applejack. When one freezes cider most of the impurities stay with the alcohol. In comparison, when one heats cider most of the impurities stay with the liquid, not the alcoholic vapor.
Fortunately modern applejack doesn't have this problem. Laird's (the only applejack producer of which I am aware) applejack consists of 35% apple brandy and 65% neutral grain spirits. In comparison, apple brandy is exactly what it sounds like.
Now you can compare apples to apples. Cheers!