Depending on your perspective, "Jersey girl" jokes are funny, stupid, and/or offensive. You won't make fun of the Jersey Girl cocktail. The late Gary "Gaz" Regan, a noted author and luminary in the cocktail community, created the Jersey Girl in 2005 in honor of the 225th anniversary of Laird & Company, which produces applejack and apple brandy. Where is Laird & Company headquartered? New Jersey.
Combine in a shaker with ice, shake with some stereotypical attitude of a you know who, and strain into a chilled glass (preferably martini or coupe). Lime slice garnish optional.
The Jersey Girl is a variation of the underrated Cosmopolitan, which is quite good if you make it properly. The Jersey Girl swaps in applejack for vodka. If you compare apples to apples, you'll know applejack is very similar to but not quite the same as apple brandy. You can use them in classics such as the Jack Rose, modern classics such as the Newark, or originals such as my American Apple. I prefer Cointreau, but you can use a different triple sec if you like. The Jersey Girl is a drink where you can compare apples to oranges, and the result is tasty. One last note -- use unsweetened cranberry juice if you can.
So what's the difference between a Jersey Girl and a Jersey girl? Think of a punchline as you savor a Jersey Girl.