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

Yes

The meaning, spelling, and grammatical function of "ainda" are identical in both Brazilian and Continental Portuguese. It functions as an adverb meaning "still," "yet," or "even." The primary difference is in pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, the vowels are often more "closed" or reduced (devoiced), which can make the word sound shorter or more clipped to a Brazilian ear.

Brazilian Portuguese Examples

1. Eu ainda não terminei o meu trabalho. (I haven't finished my work yet.)
2. Ele ainda mora com os pais. (He still lives with his parents.)
3. Você ainda quer ir ao cinema? (Do you still want to go to the movies?)
4. Isso ainda vai dar problema. (This is still going to cause trouble.)
5. Ainda tem muita gente na festa. (There is still a lot of people at the party.)

Portuguese (Continental) Examples

1. Ainda não terminei o meu trabalho. (I haven't finished my work yet.)
2. Ele ainda vive com os pais. (He still lives with his parents.)
3. Ainda queres ir ao cinema? (Do you still want to go to the movies?)
4. Isto ainda vai dar problemas. (This is still going to cause problems.)
5. Ainda há muita gente na festa. (There is still a lot of people at the party.)