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Pia vs. lava-loiça

While both pia and lava-loiça refer to a basin for washing, the primary difference lies in regional usage between Brazil and Portugal, as well as the specific location of the object within the house.

Pia

A1
In Brazilian Portuguese, pia is the universal word for a sink, used for both the pia da cozinha (kitchen sink) and the pia do banheiro (bathroom sink). In European Portuguese, pia traditionally refers to a stone basin, an animal trough, or a baptismal font in a church, rather than a modern kitchen appliance.
A pia da cozinha está,entupida com restos de comida.
(The kitchen sink is clogged with food scraps.)
Depois de escovar os dentes, limpe a pia.
(After brushing your teeth, clean the sink.)
Na antiga quinta, os animais bebiam água numa pia de pedra.
(At the old farm, the animals drank water from a stone trough.)

Lava-loiça

A2
This term is primarily used in European Portuguese to specifically denote the kitchen sink where dishes are washed. It literally implies washes-dishes and is distinct from the bathroom sink, which is usually called a lavatório in Portugal.
Por favor, não deixes a louça suja dentro do lava-loiça.
(Please do not leave dirty dishes inside the kitchen sink.)
Vamos instalar um novo lava-loiça de aço inoxidável.
(We are going to install a new stainless steel kitchen sink.)
A canalização por baixo do lava-loiça precisa de ser reparada.
(The plumbing underneath the kitchen sink needs to be repaired.)

Summary

Use pia generally in Brazil for any sink, or in Portugal for stone basins. Use lava-loiça in Portugal specifically for the kitchen sink.