Chifre vs. corno
While both corno and chifre technically mean the same thing anatomically, their usage varies significantly between Brazil and Portugal due to cultural slang. Both words can imply infidelity (referring to a cuckold), but the stigma attached to corno in Brazil makes it almost unusable for animals in daily conversation there.
Chifre
B1This refers to the hard projection on the head of animals like cattle, goats, or rhinos. It is the standard, neutral word used in Brazil for the animal part to avoid the vulgar connotations of the other term. It is also widely understood and used in Portugal.
O touro quebrou o chifre na cerca.
(The bull broke his horn on the fence.)
Rinocerontes são caçados pelo marfim de seu chifre.
(Rhinos are hunted for the ivory of their horn.)
Aquele animal tem um par de chifres enorme.
(That animal has a huge pair of horns.)
Corno
B2In Portugal, this is a standard biological term for an animal horn. However, in Brazil, corno is used almost exclusively as an offensive slang term for a person whose partner has cheated on them (a cuckold). Therefore, Brazilians rarely use corno for animals, whereas Portuguese speakers use it freely in zoological contexts.
Em Portugal, diz-se que o caracol põe os cornos ao sol.
(In Portugal, it is said that the snail puts its horns out in the sun.)
Ele toca corno inglês na orquestra.
(He plays the English horn in the orchestra.)
A cabra usou os cornos para se defender.
(The goat used its horns to defend itself.)
Summary
In short, use chifre when speaking in Brazil to refer to animal parts; corno is usually interpreted as a heavy insult there. In Portugal, corno is the standard word for the animal anatomy, though chifre is also acceptable.