Shepherd's Pie (or Cottage Pie) - what's in yours?

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Shepherd's Pie traditionally is made with lamb, while Cottage Pie is made with beef. The name Shepherd's pie eventually stuck to the beef version in the US probably because beef was more prevalent here. My mother used to make it using her leftovers from a roast beef dinner, but what she did was grind the beef and vegetables together and mix it with the gravy. Then she'd put it in a large pie pan and top it with mashed potatoes. I've only ever seen one mention of this method of making it and that person was from England. My grandfather's grandfather came over from England, so did this method come with him? Now I make mine (which my mother assured me was NOT Shepherd's Pie) with ground beef and mixed veggies and gravy. The potatoes are mixed with garlic powder, sour cream, butter and other seasonings. My daughter adds cheese, but I don't. That last is one of my questions - I've been seeing recipes all over that call for cheese in the potatoes or on top of the potatoes. I never had that at all growing up and don't use it when I make mine. It seems so out of place. So, how do you all make yours (whether beef or lamb)? Do you use pre-cooked beef that you grind or do you use ground/minced beef or lamb and a mix of veggies? What do you do?