A food dish is generally something that food is eaten or served from. It can also mean the food served or contained on a dish, such as, "I wish I had that bacon dish."
A food plate tends to refer specifically to a flat dish that is
suitable for holding food that does not have a high liquid content.
It can also mean the food served or contained on a plate, such as,
"I ate that whole bacon plate."
A food platter is a large shallow usually oval dish or plate, used
for serving food.
It is also a course of a meal, usually consisting of several
different foods served on the same plate, such as a bacon platter.
Although size does not matter for plates and dishes, some people
refer to small as dish and larger as plate. Size does matter for
platters, which are larger.
Bottom line, all plates are not platters and all platters are not
plates, but all plates and platters are dishes.