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

Yes

The word "casada" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are generally more open and the "a" sounds are more clearly articulated. In Continental Portuguese, unstressed vowels (such as the second "a" in casada) tend to be more closed, reduced, or almost swallowed, making the word sound more "clipped" or shorter to a Brazilian ear.

Brazilian Portuguese Examples

1. Ela está casada faz dois anos. (She has been married for two years.)
2. Minha irmã casada mora aqui. (My married sister lives here.) *3. Ela ficou casada com ele. (She ended up married to him.)
3. Ela é uma mulher casada e muito dedicada. (She is a married and very dedicated woman.)
4. Ela está casada e muito feliz. (She is married and very happy.)

Continental Portuguese Examples

1. Ela está casada há dois anos. (She has been married for two years.)
2. A minha irmã casada vive cá. (My married sister lives here.)
3. Ela ficou casada com ele. (She ended up married to him.)
4. Ela é uma mulher casada e muito dedicada. (She is a married and very dedicated woman.)
5. Ela está casada e muito contente. (She is married and very happy.)