I'm an American, and I too know the difference between cottage and Shepherd's pie. Some people never leave their small towns and assume their experience and limited knowledge is universal.
If I ordered shepherd's pie and it came with any meat other than mutton I'd be unhappy because it's not shepherd's pie. Maybe this is just a regional thing though, looks tasty anyway.
Australia checking in. We love our pies. Pop potato on the top? Potato pie. Chicken instead of beef? Chicken pie. Lamb pie. Curry pie. Etc.
We also have shepherds pie but frankly that’s just a shitty potato pie without the pastry.
(Tongue in cheek, having some fun at the expense of the Poms getting all hot under the collar that someone mislabelled a cottage pie. Almost as bad as the yanks.)