Is the word shorts the same in Brazilian and European Portuguese?

No

The difference between the two is in typical usage. In Brazil, "shorts" is the standard, most common term used for casual short trousers. In Portugal, while the word "shorts" is understood due to the influence of English and media, it is much more natural and common to use the word calções. Additionally, when referring to the material (denim), a Brazilian would say "jeans," whereas a Portuguese person would typically say "ganga."

Brazilian Portuguese Examples

1. Eu adoro usar shorts no calor. (I love wearing shorts in the heat.)
2. Você viu meu shorts jeans? (Did you see my denim shorts?)
3. Ele só usa shorts para ir à praia. (He only wears shorts to go to the beach.)
4. Esse shorts é muito confortável. (These shorts are very comfortable.)
5. Vou comprar uns shorts novos na promoção. (I'm going to buy some new shorts on sale.)

Continental Portuguese Examples

1. Eu adoro usar calções no calor. (I love wearing shorts in the heat.)
2. Viste os meus calções de ganga? (Did you see my denim shorts?)
3. Ele só usa calções para ir à praia. (He only wears shorts to go to the beach.)
4. Estes calções são muito confortáveis. (These shorts are very comfortable.)
5. Vou comprar uns calções novos na promoção. (I'm going to buy some new shorts on sale.)