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

Yes

The spelling, grammar, and meaning of "diferença" are identical in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated (e.g., the "e" sounds are more distinct). In Continental Portuguese, unstressed vowels are often reduced or almost "swallowed," which can make the word sound shorter or more clipped to a Brazilian ear.

Brazilian Portuguese Examples:

1. Não tem muita diferença entre os dois. (There isn't much difference between the two.)
2. Isso faz toda a diferença na minha rotina. (That makes all the difference in my routine.)
3. Qual é a diferença de preço entre esses dois? (What is the price difference between those two?)
4. Eu não vi diferença nenhuma. (I didn't see any difference.)
5. A diferença entre eles é bem grande. (The difference between them is quite large.)

Continental Portuguese Examples:

1. Não há muita diferença entre os dois. (There isn't much difference between the two.)
2. Isto faz toda a diferença na minha rotina. (This makes all the difference in my routine.)
3. Qual é a diferença de preço entre estes dois? (What is the price difference between these two?)
4. Não vi diferença nenhuma. (I didn't see any difference.)
5. A diferença entre eles é muito grande. (The difference between them is very large.)