The Whiskey Julep cocktail is part of the family of "juleps" whose most famous cocktail is the Mint Julep. These two recipes are almost identical, the only difference is that the Mint Julep is made very precisely with bourbon whisky.
If there are 2 distinct names for an almost identical recipe, it is because originally the Mint Julep was not necessarily made with whiskey. The Mint Julep was initially made with any spirits, then in 1862 in "How to mix drinks", Jerry Thomas called for it to be made with brandy and rum (more information on the Mint Julep page). The Whiskey Julep also appears in 1862 in this same book by Jerry Thomas.