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Dia de semana vs. dia útil

In Portuguese, whether you use dia de semana or dia útil depends on whether you are talking about the calendar or business operations. While both generally refer to Monday through Friday, the distinction is crucial regarding public holidays and official deadlines. These definitions hold true for both Brazilian and European Portuguese.

Dia de semana

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This term translates literally to day of the week and refers to any day from Monday to Friday. It defines the day simply by its position on the calendar, contrasting it with the fim de semana (weekend). Even if a national holiday falls on a Wednesday, that Wednesday is still technically a dia de semana because it is not a Saturday or Sunday.
Eu prefiro ir ao supermercado em dia de semana porque está mais vazio.
(I prefer going to the supermarket on a weekday because it is emptier.)
O trânsito na cidade é sempre pior em dia de semana.
(City traffic is always worse on a weekday.)
É difícil encontrar estacionamento aqui durante qualquer dia de semana.
(It is hard to find parking here during any weekday.)
As crianças têm aulas em todo dia de semana.
(The children have classes every weekday.)

Dia útil

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This term translates to useful day or working day (business day). It refers to days when commercial, financial, and government activities take place. A dia útil is any dia de semana (Monday to Friday) that is NOT a holiday. This is the standard term used for banking clearance, delivery times, and legal deadlines in both Brazil and Portugal.
O pagamento será processado em até três dias úteis.
(The payment will be processed within three business days.)
Como amanhã é feriado, não conta como dia útil.
(Since tomorrow is a holiday, it does not count as a working day.)
Você tem um prazo de cinco dias úteis para recorrer da multa.
(You have a deadline of five business days to appeal the fine.)
Sábado não é considerado dia útil para os bancos.
(Saturday is not considered a business day for banks.)

Summary

The main difference lies in holidays. A dia de semana is simply a calendar definition (Monday through Friday), whereas a dia útil is a functional definition (Monday through Friday, excluding holidays). If Christmas falls on a Tuesday, that Tuesday is a dia de semana (it is not the weekend), but it is not a dia útil (banks and offices are closed).