Here in the states we are more of a beef eating culture than a lamb eating one, and when one is served “shepherd’s pie” here, it is most often made with ground beef. In Australia they would call the beef dish a “cottage pie” and the lamb dish “shepherd’s pie”.
Regardless of what you call it, a shepherd’s pie is basically a casserole with a layer of cooked meat and vegetables, topped with mashed potatoes, and baked in the oven until the the mashed potatoes are well browned. When you dig in you get a spoonful of mashed potatoes, some crispy bits, meat, and vegetables all in one bite. It’s pure comfort food.