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

Yes

The word "ajuda" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The differences between the two variants are found in pronunciation and sentence syntax:

• Pronunciation: In Brazilian Portuguese, the vowels are typically more "open" and the rhythm is more melodic. In Continental Portuguese, unstressed vowels (such as the "a" at the beginning and end of "ajuda") are often "reduced" or "closed," making them sound much shorter or nearly silent.
• Syntax: While the word itself does not change, the way it interacts with object pronouns in a sentence differs. Brazilians naturally place pronouns before the verb (próclise), such as "me ajuda," whereas Portuguese speakers naturally place them after the verb (ênclise), such as "ajuda-me."

Brazilian Portuguese Examples

1. Eu preciso de ajuda com o trabalho. (I need help with the work.)
2. Você pode me dar uma ajuda aqui? (Can you give me a hand here?)
3. A ajuda dele foi fundamental. (His help was fundamental.)
4. Ela sempre me ajuda nos estudos. (She always helps me with my studies.)
5. Muito obrigado pela sua ajuda. (Thank you very much for your help.)

Continental Portuguese Examples

1. Preciso de ajuda com o trabalho. (I need help with the work.)
2. Podes dar-me uma ajuda aqui? (Can you give me a hand here?)
3. A ajuda dele foi fundamental. (His help was fundamental.)
4. Ela ajuda-me sempre nos estudos. (She always helps me with my studies.)
5. Muito obrigado pela tua ajuda. (Thank you very much for your help.)