The cottage pie and shepherd's pie are not the same thing although they are similar.
The main difference though between the cottage pie and shepherd's pie is in the meat that is used to make the pies.
Cottage Pie is made with lamb meat while Shepherd's Pie is made with beef.
Shepherd's Pie is also sometimes called Chinese Pie.
The reason it's called Chinese Pie is because the French-Canadian railway workers liked the new concoction, adopted the dish, and called it “pâté chinois”
The words pâté chinois translates to and means Chinese Pie so that's why it's called Chinese Pie.
Also most of the workers ate their meat, potatoes and corn separately but workers of mainly Asian origins, combined their rations to create shepherd's pie, a more communal dish.
Chinese Pie is also known as Shepherds Pie and can be an adaptation of "Shepherd's Pie", but one possible explanation for the Chinese reference is that it was introduced to Canadian railway workers by Chinese cooks during the building of the North American railroads in the late 19th century.
Either way you can call Chinese Pie Shepherd's Pie if you want too or simply call it Chinese Pie.