What is the difference between Cottage Pie, Shepherd's Pie and Cumberland Pie?

Tweet

Shout out to all those in the UK! I'm not from the UK myself, and upon visiting my mother I found the above three (store bought) in her fridge. I cannot tell the difference and I am mystified. To me it just seems like mince with gravy and veg with mashed potatoes on top (optional cheese) baked in an oven. What am I missing, myLot? Are the recipes any different? The only one that seemed to stand out a little was Cumberland's (the potato to mince ratio was atrocious and it had delicious cheese on top which made it taste a little different). So what is classified as the above? Please, enlighten me. I'm very confused.