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

No

While the meaning, spelling, and fundamental definition of "ajudar" are identical in both dialects, there are significant differences in grammar (syntax) and pronunciation:

• Grammar/Usage (Pronoun Placement): This is the most notable difference. In Brazilian Portuguese (BP), it is extremely common and natural to place object pronouns before the verb (proclisis), such as "Eu te ajudo" (I help you). In Continental Portuguese (PT-PT), placing the pronoun before the verb in this way is considered grammatous/incorrect in standard speech; instead, the pronoun follows the verb (enclisis), as in "Eu ajudo-te."
• Pronunciation: In Brazil, the vowels in "ajudar" tend to be more open and the "r" at the end can vary significantly by region (often sounding like an "h" in many dialects). In Portugal, the pronunciation is more closed and consonant-heavy, with a more distinct, retroflex, or tapped "r."

Brazilian Portuguese Examples

1. Eu vou te ajudar com a lição de casa. (I am going to help you with the homework.)
2. Você pode me ajudar aqui rapidinho? (Can you help me here very quickly?)
3. A gente sempre ajuda os nossos vizinhos. (We always help our neighbors.)
4. Eu preciso que você me ajude a carregar isso. (I need you to help me carry this.)
5. Ela te ajuda sempre que você precisa. (She helps you whenever you need it.)

Continental Portuguese Examples

1. Eu vou ajudar-te com o trabalho de casa. (I am going to help you with the homework.)
2. Podes ajudar-me aqui um momento? (Can you help me here for a moment?)
3. Nós sempre ajudamos os nossos vizinhos. (We always help our neighbors.)
4. Preciso que me ajudes a carregar isto. (I need you to help me carry this.)
5. Ela ajuda-te sempre que precisas. (She helps you whenever you need it.)