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

Yes

The word "médica" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference lies in pronunciation.

• Brazilian Portuguese: The vowels are generally more open, and the rhythm is more "syllable-timed," meaning each syllable receives a relatively clear and distinct articulation.
• Continental Portuguese: The vowels—especially unstressed ones—tend to be more closed or "reduced." The rhythm is more "stress-timed," which can make the word sound more clipped or denser to a Brazilian ear.

Brazilian Portuguese Examples

1. A médica me deu um atestado. (The doctor gave me a medical certificate.)
2. Preciso marcar uma consulta com a minha médica. (I need to schedule an appointment with my doctor.)
3. A médica explicou tudo direitinho. (The doctor explained everything very clearly.)
4. Ela trabalha como médica num hospital grande. (She works as a doctor in a large hospital.)
5. A médica passou um remédio para mim. (The doctor prescribed a medicine for me.)

Continental Portuguese Examples

1. A médica deu-me uma baixa. (The doctor gave me sick leave.)
2. Tenho de ligar para a médica pelo telemóvel. (I have to call the doctor on the mobile phone.)
3. A médica explicou-me o diagnóstico. (The doctor explained the diagnosis to me.)
4. A médica receitou este medicamento. (The doctor prescribed this medication.)
5. A médica é muito competente. (The doctor is very competent.)