Cupim vs. térmite
The primary difference between cupim and térmite lies in regional usage and versatility. While cupim is the exclusive term in Brazil and carries multiple meanings, térmite is standard in Portugal, Africa, and scientific contexts.
Cupim
B1In Brazilian Portuguese, cupim is the everyday word for the termite insect. Uniquely, it also refers to the physical earthen nest (mound) the insects build, and it is the name of a popular, fatty cut of beef (the hump of Zebu cattle) in Brazilian cuisine.
Descobrimos que a porta do quarto está cheia de cupim.
(We discovered that the bedroom door is full of termites.)
O fazendeiro precisou remover o cupim que estava no meio do pasto.
(The farmer needed to remove the termite mound that was in the middle of the pasture.)
Vou preparar um cupim assado para o almoço de domingo.
(I will prepare a roasted beef hump for Sunday lunch.)
Eles chamaram a dedetizadora para acabar com o cupim.
(They called the pest control company to get rid of the termites.)
Térmite
B2This is the standard term for the insect used in European Portuguese (Portugal) and African Lusophone countries. It is derived from Latin and is also strictly used in scientific or academic papers to describe the species, regardless of the region.
A térmite é conhecida pela capacidade de digerir celulose.
(The termite is known for its ability to digest cellulose.)
Encontraram vestígios de térmite na estrutura antiga do prédio em Lisboa.
(They found traces of termites in the old structure of the building in Lisbon.)
O artigo científico descreve o comportamento social da térmite.
(The scientific article describes the social behavior of the termite.)
As colónias de térmites podem causar grandes prejuízos materiais.
(Termite colonies can cause major material damage.)
Summary
In short, use cupim if you are in Brazil or referring to the specific cut of meat or the mound. Use térmite if you are in Portugal, Lusophone Africa, or writing a formal biological text.