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Avión vs. aeroplano

In Spanish, both avión and aeroplano translate to airplane or aeroplane. The main difference between them lies in their frequency of use and connotation, with one being the modern standard and the other being more dated or specialized.

Avión

A1
This is the most common, universal, and modern word for airplane. It is used in all situations, from everyday conversation and travel to technical and official contexts. It is the default and most natural choice in contemporary Spanish.
Mi vuelo sale en una hora, tengo que abordar el avión pronto.
(My flight leaves in an hour, I have to board the plane soon.)
¿Viste ese avión de combate pasar tan rápido?
(Did you see that fighter jet pass by so fast?)
Compramos los boletos de avión con mucha anticipación.
(We bought the plane tickets well in advance.)
El nuevo avión presidencial es mucho más grande.
(The new presidential airplane is much bigger.)
Un avión de papel no vuela tan lejos como uno de verdad.
(A paper airplane doesn't fly as far as a real one.)

Aeroplano

B1
This word also means airplane, but it is much less common in everyday speech. It often sounds old-fashioned, technical, or poetic. It is typically used when referring to early aircraft, in historical contexts, or by children, similar to the distinction between airplane and aeroplane in English.
El museo tiene una exhibición del primer aeroplano que cruzó el océano.
(The museum has an exhibition of the first aeroplane that crossed the ocean.)
Mi abuelo solía construir modelos de aeroplano de la Primera Guerra Mundial.
(My grandfather used to build model aeroplanes from the First World War.)
En el libro antiguo, el héroe escapa en un pequeño aeroplano.
(In the old book, the hero escapes in a small aeroplane.)
El niño jugaba con un aeroplano de juguete en el jardín.
(The little boy was playing with a toy aeroplane in the garden.)
El diseño del aeroplano ha evolucionado mucho desde su invención.
(The design of the aeroplane has evolved a lot since its invention.)

Summary

In summary, use avión for all general and modern purposes. It is the standard, everyday word for airplane in Spanish. Use aeroplano primarily for historical contexts, to refer to early aircraft, or to achieve a specific vintage or technical tone. For daily communication, avión is always the correct choice.