Brasileño vs. brasilero
Both brasileño and brasilero translate to Brazilian in English. They are completely synonymous in meaning, but they differ primarily in their geographical usage and level of formality.
Brasileño
The word brasileño is the standard and formally preferred term for someone or something from Brazil. It is the most widely accepted variation globally and is heavily preferred in Spain, Mexico, and formal or academic contexts.
El gobierno brasileño anunció nuevas medidas económicas para la región.
(The Brazilian government announced new economic measures for the region.)
La música de ese artista brasileño ha ganado popularidad en Europa.
(The music of that Brazilian artist has gained popularity in Europe.)
Mi hermana conoció a un estudiante brasileño durante su intercambio.
(My sister met a Brazilian student during her exchange.)
Las exportaciones de café brasileño aumentaron significativamente este año.
(Brazilian coffee exports increased significantly this year.)
Quiero aprender a cocinar un plato tradicional brasileño para la fiesta.
(I want to learn to cook a traditional Brazilian dish for the party.)
El equipo brasileño demostró una técnica superior en el campeonato.
(The Brazilian team demonstrated superior technique in the championship.)
Las playas del noreste brasileño son elogiadas por su belleza natural.
(The beaches of the Brazilian northeast are praised for their natural beauty.)
Brasilero
The word brasilero is a regional variant adopted directly from the Portuguese word for Brazilian. It is widely recognized and accepted, but it is deeply rooted in everyday, casual speech across South American countries such as Argentina, Uruguay, Chile, Colombia, and Peru.
Mi amigo brasilero me enseñó los pasos básicos para bailar samba.
(My Brazilian friend taught me the basic steps to dance samba.)
Fuimos a cenar a un excelente restaurante brasilero en Buenos Aires.
(We went to dinner at an excellent Brazilian restaurant in Buenos Aires.)
El acento brasilero me resulta muy melódico y fácil de reconocer.
(I find the Brazilian accent very melodic and easy to recognize.)
Compró un termo brasilero de muy buena calidad para llevar al viaje.
(She bought a very good quality Brazilian thermos to take on the trip.)
Los hinchas del club brasilero llenaron el estadio en pocos minutos.
(The fans of the Brazilian club filled the stadium in a few minutes.)
Si cruzas la frontera, puedes comprar chocolate brasilero muy barato.
(If you cross the border, you can buy very cheap Brazilian chocolate.)
Vimos un documental espectacular sobre el carnaval brasilero anoche.
(We watched a spectacular documentary about the Brazilian carnival last night.)
Summary
In short, both brasileño and brasilero are correct and mean exactly the same thing. You should choose brasileño for formal situations or when speaking in Spain and Mexico. On the other hand, brasilero is a natural, conversational choice if you are interacting with people from South America, as it directly mirrors the Portuguese pronunciation.