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

No

The difference lies in typical usage. In Brazil, "calçada" is the standard, generic term for any sidewalk or pavement used by pedestrians. In Portugal, while "calçada" is used, it frequently refers specifically to the "calçada portuguesa" (the traditional, decorative black-and-white stone mosaic). For the general pedestrian walkway or sidewalk, a Portuguese person is much more likely to use the word passeio.

Brazilian Portuguese Examples

1. A calçada está muito esburacada. (The sidewalk is very potholed.)
2. Cuidado para não tropeçar na calçada. (Be careful not to trip on the sidewalk.)
3. Vou varrer a calçada hoje à tarde. (I am going to sweep the sidewalk this afternoon.)
4. A calçada da frente da casa está bem limpa. (The sidewalk in front of the house is very clean.)
5. O carro subiu na calçada. (The car drove up onto the sidewalk.)

Continental Portuguese Examples

1. Não se pode estacionar no passeio. (You cannot park on the sidewalk.)
2. O passeio está muito estreito nesta rua. (The sidewalk is very narrow on this street.)
3. Adoro caminhar pela calçada portuguesa. (I love walking on the Portuguese pavement.)
4. O passeio está ocupado por esplanadas. (The sidewalk is occupied by outdoor seating.)
5. O passeio está molhado devido à chuva. (The sidewalk is wet due to the rain.)