Avião vs. aeroplano
In Portuguese, both avião and aeroplano translate to airplane or aeroplane. However, their usage is very different. Avião is the modern, standard word used by everyone, while aeroplano is a much less common term that sounds formal, technical, or even old-fashioned.
Avião
A1This is the universal, everyday word for airplane. It is used in all contexts, from casual conversations to technical documents, and is the term you will hear and use 99% of the time in both European and Brazilian Portuguese.
O nosso voo atrasou e perdemos o avião para o Rio de Janeiro.
(Our flight was delayed and we missed the plane to Rio de Janeiro.)
As crianças adoram fazer um avião de papel na escola.
(Children love to make a paper airplane at school.)
Aquele é um avião militar ou comercial?
(Is that a military or a commercial airplane?)
A manutenção do avião é essencial para a segurança dos passageiros.
(The airplane's maintenance is essential for passenger safety.)
Eu comprei um modelo em miniatura do meu avião favorito.
(I bought a miniature model of my favorite airplane.)
Aeroplano
B2This is a formal, technical, or archaic term for airplane. It is rarely used in modern conversation and often carries a historical connotation, referring to early aircraft, or is used in a very specific scientific or literary context.
O museu exibe um aeroplano do início do século XX.
(The museum displays an aeroplane from the early 20th century.)
O livro descreve a construção do primeiro aeroplano de Santos Dumont.
(The book describes the construction of Santos Dumont's first aeroplane.)
O engenheiro explicou os princípios de voo de um aeroplano.
(The engineer explained the principles of flight of an aeroplane.)
No filme antigo, o herói pilotava um pequeno aeroplano vermelho.
(In the old movie, the hero flew a small red aeroplane.)
A palavra 'aeroplano' soa muito mais formal do que 'avião'.
(The word aeroplano sounds much more formal than avião.)
Summary
In essence, always use avião for airplane in any normal situation. Use aeroplano only if you want to sound deliberately historical, highly technical, or formal, as it is not part of everyday modern Portuguese vocabulary.