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

No.

While the fundamental meaning of "régua" (a measuring tool) remains the same, there is a significant difference in typical usage due to Brazilian slang. In Brazil, the expression "na régua" is frequently used in urban culture (such as Funk or Trap) to describe something that is perfectly aligned, very sharp, precise, or looking excellent. In Portugal, "régua" is almost exclusively used to refer to the physical object. Additionally, there are subtle differences in pronunciation, specifically in the vowel quality and the way unstressed vowels are reduced.

Brazilian Portuguese Examples:

1. Preciso de uma régua para desenhar essa linha. (I need a ruler to draw this line.)
2. A régua de trinta centímetros sumiu. (The thirty-centimeter ruler disappeared.)
3. O corte de cabelo dele está na régua. (His haircut is perfect/sharp.)
4. Use a régua para medir o papel. (Use the ruler to measure the paper.)
5. Essa régua está quebrada. (This ruler is broken.)

Continental Portuguese Examples:

1. Preciso de uma régua para desenhar esta linha. (I need a ruler to draw this line.)
2. A régua de trinta centímetros desapareceu. (The thirty-centimeter ruler disappeared.)
3. O corte de cabelo dele está impecável. (His haircut is impeccable.)
4. Usa a régua para medir o papel. (Use the ruler to measure the paper.)
5. Esta régua está partida. (This ruler is broken.)