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

No

While the spelling and fundamental meaning of "desculpa" (as both a noun meaning "an excuse" and a verb meaning "to apologize") are identical, there are significant differences in typical usage and formality.

In Brazilian Portuguese, "desculpa" is used very broadly and informally to mean both "sorry" and "excuse me" (to get someone's attention or after a small mistake) across most social levels. In Continental Portuguese, "desculpa" is strictly informal, used only when addressing someone as tu (friends or family). For strangers, elders, or professional settings, a Portuguese person will almost always use the more formal "desculpe." Furthermore, while a Brazilian might use "desculpa" to navigate through a crowded space, a Portuguese person is much more likely to use "com licença" for that specific purpose.

Brazilian Portuguese Examples:

1. Desculpa o atraso, o trânsito estava horrível. (Sorry for the delay, the traffic was horrible.)
2. Desculpa, você pode repetir o que disse? (Sorry, can you repeat what you said?)
3. Mil desculpas por ter esquecido seu aniversário. (A thousand apologies for forgetting your birthday.)
4. Desculpa, tem como você me ajudar aqui? (Excuse me, is there a way you can help me here?)
5. Não foi por mal, me desculpa! (I didn't mean it, forgive me!)

Continental Portuguese Examples:

1. Desculpe o atraso, o trânsito estava terrível. (Sorry for the delay, the traffic was terrible.)
2. Desculpe, não percebi o que disse. (Sorry, I didn't understand what you said.)
3. Com licença, gostaria de passar por aqui. (Excuse me, I would like to pass through here.)
4. Peço desculpa pelo incómodo causado. (I apologize for the inconvenience caused.)
5. Desculpe-me, pode ajudar-me com isto? (Excuse me, can you help me with this?)