"Chinese Pie" is a French Canadian—and later New England—name for a pie or casserole made with layers of ground beef, corn, and potatoes.
The Chinese pie is very similar to a cottage pie or shepherd's pie.
Pâté chinois is a Québécois dish typically containing ground beef, corn (or cream of corn) and mashed potatoes, and served with ketchup.
Shepherd's pie is an English version, made with lamb, and definitely with no corn.
There are other variations, including hachis parmentier, a French version.