A dish is something you serve food on. It can be for one person or many. A platter is something bigger you serve food on. Food served on a platter is often meant to be shared. For example, you might bring a cheese platter or a cookie platter to a party for many people to share.

The dish is like a plate. For example, "Clean the dishes". Dish can also mean like "These dishes are all Mexican". The platter would be like a very big plate, basically a bigger version of a dish. It can also mean there is a lot of food on that plate. I would never use any of these words when describing food. The platter is very formal and can be used to replace dish informal situations. For the word "Dish", I would only use that when describing the plate itself. I would never use them for "measuring stuff" like "A dish of food". I would use it like "Clean the dishes". If you want to say "A dish of food" or a "platter of food" in a more informal way, say "plate". "A plate of food" would sound a lot better. Even as natives, I struggle to tell the difference between "Dish" and "platter".

A platter is usually a big plate that might have enough food for several people. A plate is "un plato" for one person usually. It might be big (for a whole meal), or small (for a salad, bread, or dessert). It can also mean a ceramic container used in baking. "Dish" has several meanings. A dish is sometimes a plate or a platter. ("Put the dishes on the table.) But it's also sometimes a plate including the food or a particular kind of food. "Paella is one of my favourite dishes." Also, "dishes" as a plural can refer to all the plates, bowls, glasses, and cutlery used to serve a meal: "After dinner, I washed the dishes." One slang usage for "dish" is "a pretty girl": "She's a real dish."