I’ve made it with beef, lamb, pork - never tried minced chicken or turkey, vegetarian options (mushroom and eggplant is great).
On of the best things I ever bought was a giant baking pan - far too big for our 4-person family. That means whenever I make it, there is always heaps of leftovers (and there’s only one thing better than today’s shepherd’s pie…)
Star-gazer pie, with whole fishes? Heads poking out looking up, and maybe tails, too. That’s a whole different thing from a casserole with mashed potatoes.
The older of the two terms is cottage pie which OED defines as “a dish of minced beef baked under mashed potatoes” with a first cite from 1791.
Shepherd’s pie has a more general definition as regarding the main ingredient, “a pie consisting of chopped meat and potatoes, covered with a crust of mashed potatoes browned”, the earliest cite they give being 1877.