Plato vs. platillo
In Spanish, both plato and platillo can translate to dish when referring to prepared food, but they carry different nuances. The word plato is the standard, universal term for a regular meal or a course within a meal. On the other hand, platillo literally translates to small plate and is often used to describe smaller portions, appetizers, side dishes, or special culinary delicacies. Additionally, platillo is used much more frequently in certain Latin American countries, like Mexico, to refer to any prepared recipe, whereas plato is universally understood everywhere.
Plato
The word plato is the most common and general term used to describe a standard dish, course, or full meal of prepared food.
La paella es un plato tradicional muy famoso en España.
(Paella is a very famous traditional dish in Spain.)
El camarero nos recomendó el plato principal del día.
(The waiter recommended the main dish of the day to us.)
Mi abuela siempre prepara un plato de sopa caliente para la cena.
(My grandmother always prepares a dish of hot soup for dinner.)
Ese restaurante italiano sirve un plato de pasta increíble.
(That Italian restaurant serves an incredible pasta dish.)
Los invitados elogiaron el plato vegetariano que cocinaste.
(The guests praised the vegetarian dish that you cooked.)
Platillo
The word platillo is used to describe a smaller dish, an appetizer, a delicate culinary creation, or a specific local recipe, especially in Latin American Spanish.
Para empezar, pedimos un platillo de quesos y aceitunas.
(To start, we ordered a small dish of cheeses and olives.)
El chef creó un platillo exótico con ingredientes locales.
(The chef created an exotic dish with local ingredients.)
Sirvieron un platillo ligero antes de traer la carne.
(They served a light dish before bringing the meat.)
Los tacos al pastor son un platillo muy popular en México.
(Tacos al pastor are a very popular dish in Mexico.)
En la boda ofrecieron varios platillos deliciosos para degustar.
(At the wedding they offered several delicious dishes to taste.)
Summary
To summarize, you should use plato when talking about a standard, regular-sized meal or main course, as it is the most universally understood term. You should opt for platillo when referring to a smaller portion, an appetizer, a delicate delicacy, or when speaking about specific local recipes in places like Mexico.