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Pedir vs. ordenar

While both pedir and ordenar can be translated as "to order," they are not interchangeable. Pedir is the standard and most common choice for ordering food and drinks, implying a request. Ordenar is more formal and primarily means "to command" or "to organize," and using it for food can sound unnatural or overly authoritative.

Pedir

A1
Pedir is the go-to verb for ordering in everyday situations, especially for food, drinks, or services. It translates best to "to ask for" or "to request," making it the polite and natural choice in a restaurant or when making a purchase.
Voy a pedir una pizza para cenar.
(I am going to order a pizza for dinner.)
¿Están listos para pedir la comida?
(Are you ready to order the food?)
Quisiera pedir un café con leche, por favor.
(I would like to order a coffee with milk, please.)
Pedimos un taxi para ir al aeropuerto.
(We ordered a taxi to go to the airport.)
Mi hermana pidió ese vestido por internet.
(My sister ordered that dress online.)
Si necesitas algo, solo tienes que pedirlo.
(If you need anything, you just have to ask for it.)

Ordenar

A2
Ordenar carries a stronger meaning of "to command," "to give an order," or "to put in order/organize." While it can be used for commercial orders (like a company buying supplies), it's far less common for food and can sound bossy or overly formal. Its primary uses are unrelated to ordering in a restaurant.
El capitán ordenó a los marineros que subieran las velas.
(The captain ordered the sailors to raise the sails.)
Tengo que ordenar todos los libros en el estante.
(I have to organize all the books on the shelf.)
La empresa va a ordenar cien nuevos monitores.
(The company is going to order one hundred new monitors.)
El juez le ordenó al acusado que se pusiera de pie.
(The judge ordered the defendant to stand up.)
Por favor, ayúdame a ordenar los documentos por fecha.
(Please, help me sort the documents by date.)
El gerente ordenó un informe detallado sobre las ventas.
(The manager ordered a detailed report on the sales.)

Summary

In short, always use pedir when ordering food, drinks, or common services like a taxi; it is the natural and polite word for making a request. Reserve ordenar for its primary meanings: giving a command (like a general or a judge), or organizing things (like a room or files). While ordenar can be used for large, formal purchase orders, using it for a coffee will make you sound out of place.