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

No

While the word "cachoeira" is grammatically correct and understood in both dialects, there is a difference in typical usage. In Brazil, "cachoeira" is the standard, everyday word used to describe a waterfall. In Portugal, the word "cascata" is much more common and natural. While a Portuguese person might use "cachoeira," it would sound distinctly Brazilian; a local would almost instinctively reach for "cascata." Additionally, certain surrounding vocabulary often changes (such as "trilha" in Brazil becoming "trilho" in Portugal).

Brazilian Portuguese Usage

1. Eu amo nadar na cachoeira. (I love swimming in the waterfall.)
2. A trilha leva até uma cachoeira linda. (The trail leads to a beautiful waterfall.)
3. A cachoeira está muito forte depois da chuva. (The waterfall is very strong after the rain.)
4. Vamos fazer um piquenique perto da cachoeira? (Shall we have a picnic near the waterfall?)
5. A água da cachoeira é muito gelada. (The water from the waterfall is very cold.)

Continental Portuguese Usage

1. Eu adoro nadar na cascata. (I love swimming in the waterfall.)
2. O trilho leva a uma cascata deslumbrante. (The trail leads to a stunning waterfall.)
3. A cascata está muito caudalosa depois da chuva. (The waterfall is very powerful after the rain.)
4. Vamos fazer um piquenique junto à cascata? (Shall we have a picnic by the waterfall?)
5. A água da cascata é geladíssima. (The water from the waterfall is extremely cold.)