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

No

While the spelling and the core technical meanings (such as computer software or a television show) are identical, the word differs in usage and pronunciation.

In Brazilian Portuguese, "programa" is frequently used colloquially to refer to social plans or "what one is doing" (e.g., "What is the plan for tonight?"). In Continental Portuguese, using "programa" in this context would sound as if you are referring to a formal, structured itinerary or a TV schedule; instead, a Portuguese person would naturally use the word "planos". Additionally, the pronunciation differs: Brazilians typically use a more open "o" [pɾo], while Portuguese speakers often use a more closed, reduced vowel [pɾu].

Brazilian Portuguese

1. Qual é o programa de hoje? (What is the plan for today?)
2. Não tenho programa para o fim de semana. (I don't have any plans for the weekend.)
3. Este programa de computador é muito lento. (This computer program is very slow.)
4. Eu gosto muito desse programa de TV. (I like that TV show very much.)
5. O programa de estudos mudou. (The study program changed.)

Continental Portuguese

1. Quais são os planos para hoje? (What are the plans for today?)
2. Não tenho planos para o fim de semana. (I don't have any plans for the weekend.)
3. Este programa de computador é muito lento. (This computer program is very slow.)
4. Eu gosto muito deste programa de televisão. (I like this television program very much.)
5. O plano de estudos mudou. (The study plan changed.)