The word "Cursing" in Arabic means "asking Allah to remove his mercy from this person/thing". So logically, the idea that (Dua'a == cursing) is wrong. because you can't do anything other than wishing someone to be kicked out from the mercy of Allah.
Now there are 2 types of cursing:
1.Cursing the infidels and sinners in general. it is permissible
2.Cursing a specific or particular person. Scholars have divided into 3 groups:
- Not allowed at all.
- Only infidels but not sinners
- It is permissible
and each of these froups have their own evidence and sources that back up their opinions
But Then you look at the hadiths of the prophet Mohammed (PBUH) and what he ask us to be like :
Prophet Mohammed prohibited Muslims to cures,
Ahmad in his Musnad and Imam al-Tirmidhi in his Jaami’ from ‘Alqamah that ‘Abd-Allaah ibn Mas’ood (may Allaah be pleased with him) said:
The Messenger of Allaah (peace and blessings of Allaah be upon him) said: "The believer is not a slanderer, one who curses a great deal, one who indulges in obscenity or who in engages in foul talk."
Al-Tirmidhi said: It is a hasan ghareeb hadeeth.
2rd hadith,
Muslim (2599) narrated that Abu Hurayrah (may Allaah be pleased with him) said: It was said: O Messenger of Allaah, pray against the mushrikeen. He said: “I was not sent to curse, rather I was sent as a mercy.”
3rd Haith,
(2597) narrated from Abu Hurayrah (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: "It is not appropriate for a sincere believer to be given to cursing."
4th hadith,
2598) narrated that Abu’l-Darda’ (may Allaah be pleased with him) said: I heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say: "Those who curse a great deal will not be witnesses or intercessors on the Day of Resurrection."
Now take a note of this hadith,
it was narrated in al-Saheehayn from Thaabit ibn al-Dahhaak that:
the Prophet (peace and blessings of Allaah be upon him) said: “Cursing a believer is like killing him.”
So you are not allowed to curse those who Allah and his prophet's didn't curse in the Quran and the hadith. If you curse anyone other than those mentioned then:
Narrated by Abu’l-Darda’ (may Allaah be pleased with him) who said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: "When a person curses something, the curse ascends to heaven, and the gates of heaven are closed to it. Then it comes back down to earth and the gates of earth are closed to it. Then it looks right and left, and if it does not find anywhere to go, it goes to the one who was cursed, and if he deserves it (it befalls him), otherwise it goes back to the one who uttered it."
Narrated by Abu Dawood in his Sunan.