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Travesseiro vs. almofada

The Portuguese words travesseiro and almofada both refer to soft objects used for support, but their usage varies significantly between Brazil and Portugal. In Brazil, the distinction is strictly based on function (sleeping vs. decoration), while in Portugal, one term is much more generic than the other.

Travesseiro

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In Brazilian Portuguese, travesseiro is exclusively the object under your head when you sleep in a bed. In European Portuguese, travesseiro typically refers to a specific type of long, cylindrical or rectangular bolster that spans the width of the bed, rather than the standard individual pillow.
Eu preciso de um travesseiro novo porque o meu está muito velho.
(I need a new pillow because mine is very old.)
O médico recomendou um travesseiro mais firme para o pescoço.
(The doctor recommended a firmer pillow for the neck.)
Coloquei o travesseiro na cama antes de dormir.
(I put the pillow on the bed before going to sleep.)
Este hotel oferece um menu de travesseiros para os hóspedes.
(This hotel offers a pillow menu for the guests.)

Almofada

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In Brazilian Portuguese, almofada means a cushion used for decoration on sofas or as seat padding, but never for sleeping in a bed. However, in European Portuguese, almofada is the universal term used for both the decorative cushion on the couch and the pillow you sleep on at night.
Compramos almofadas coloridas para decorar a sala.
(We bought colorful cushions to decorate the living room.)
Em Portugal, a maioria das pessoas dorme com a cabeça numa almofada.
(In Portugal, most people sleep with their head on a pillow.)
O gato estava dormindo em cima da almofada do sofá.
(The cat was sleeping on top of the sofa cushion.)
Troque a fronha da almofada antes dos convidados chegarem.
(Change the pillowcase of the cushion before the guests arrive.)

Summary

The main difference lies in geography and utility: in Brazil, use travesseiro for sleeping and almofada for the sofa. In Portugal, use almofada for almost everything (bed and sofa), reserving travesseiro mainly for long bolsters.