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

No.

While the fundamental meaning and grammar of "médio" remain the same, there is a difference in typical usage regarding the education system. In Brazil, "ensino médio" is the standard term for high school, but in Portugal, the word "médio" is not used in this context; instead, the term "ensino secundário" is used. Additionally, there is a difference in pronunciation: Brazilian Portuguese features more open and clearly articulated vowels, while European Portuguese features more reduced or "closed" vowel sounds.

Brazilian Portuguese Examples

1. "Eu comprei uma camiseta de tamanho médio." (I bought a medium-sized t-shirt.)
2. "Ele terminou o ensino médio no ano passado." (He finished high school last year.)
3. "O desempenho dele foi médio." (His performance was average.)
4. "Estamos planejando algo de médio prazo." (We are planning something for the medium term.)
5. "A temperatura está média para esta época do ano." (The temperature is average for this time of year.)

European Portuguese Examples

1. "Eu comprei uma t-shirt de tamanho médio." (I bought a medium-sized t-shirt.)
2. "Ele terminou o ensino secundário no ano passado." (He finished high school last year.)
3. "O desempenho dele foi médio." (His performance was average.)
4. "Estamos a planear algo de médio prazo." (We are planning something for the medium term.)
5. "A temperatura está média para esta época do ano." (The temperature is average for this time of year.)