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

Yes

The word "escada" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, vowels are typically more open and clearly articulated. In Continental Portuguese, there is a much higher degree of vowel reduction, meaning unstressed vowels are often "swallowed" or shortened, and the letter "s" (when appearing before certain consonants) is more frequently pronounced with a "sh" sound.

Brazilian Portuguese Examples

1. Eu estou subindo a escada. (I am going up the stairs.)
2. A escada está muito escorregadia. (The stairs are very slippery.)
3. Ele quebrou o degrau da escada. (He broke the step of the stairs.)
4. Você precisa de uma escada? (Do you need a ladder?)
5. A escada de madeira está velha. (The wooden staircase is old.)

Continental Portuguese Examples

1. Eu estou a subir a escada. (I am going up the stairs.)
2. A escada está muito escorregadia. (The stairs are very slippery.)
3. Ele partiu o degrau da escada. (He broke the step of the stairs.)
4. Tu precisas de uma escada? (Do you need a ladder?)
5. A escada de madeira está velha. (The wooden staircase is old.)