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

Yes

The word "aranhas" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the unstressed vowels are typically more open and clearly articulated. In Continental Portuguese, there is a much stronger tendency toward vowel reduction, meaning the unstressed vowels (such as the final "a" in "aranhas") are pronounced more closed or are often nearly swallowed.

Brazilian Portuguese examples:

1. Eu vi duas aranhas no meu quarto. (I saw two spiders in my room.)
2. Tem muitas aranhas no jardim. (There are many spiders in the garden.)
3. As aranhas estão fazendo uma teia gigante. (The spiders are making a giant web.)
4. Eu tenho muito medo de aranhas. (I am very afraid of spiders.)
5. Aquelas aranhas são bem pequenas. (Those spiders are quite small.)

Portuguese (Portugal) examples:

1. Vi duas aranhas no meu quarto. (I saw two spiders in my room.)
2. Há muitas aranhas no jardim. (There are many spiders in the garden.)
3. As aranhas estão a fazer uma teia gigante. (The spiders are making a giant web.)
4. Tenho muito medo de aranhas. (I am very afraid of spiders.)
5. Aquelas aranhas são muito pequenas. (Those spiders are very small.)