The taraweeh salah for women is sunnat or nafil?
Just want to clear it more that when a girl is performing the taraweeh salah then we wilk the girl will perform it as sunnat salah or nafil salah
Is there a difference between sunna and nafl?
For me it is the same, maybe only under some circumstances in (technical term) fiqh language اصطلاح الفقهاء it makes a slight difference of the level of tawab (rewards). But for example all nafl is sunnah!
And in general Nafl=Sunnah (they are synonyms) as it is a kind of "extra or optional worship" the Messenger of Allah (peace be upon him) made which is not prescribed by Allah in the Qur'an...
This meaning can be concluded from the following Hadith:
On the authority of Abu Hurayrah (may Allah be pleased with him) who said: The Messenger of Allah (peace and blessings of Allah be upon him) said, “Verily Allah ta’ala has said: ‘Whosoever shows enmity to a wali (friend) of Mine, then I have declared war against him. And My servant does not draw near to Me with anything more loved to Me than the religious duties I have obligated upon him. And My servant continues to draw near to me with nafil (supererogatory) deeds until I Love him. When I Love him, I am his hearing with which he hears, and his sight with which he sees, and his hand with which he strikes, and his foot with which he walks. Were he to ask [something] of Me, I would surely give it to him; and were he to seek refuge with Me, I would surely grant him refuge.’ ” Al-Bukhari
Now to your questions:
When it comes to worshiping acts then any basic kind of worship (prayer, fast, hajj, zakat etc.) which is prescribed or lawful for a man has the same level of prescription for a woman. With one note for optional worships: If the husband doesn't allow his wife to perform a optional worship, for some reasonable matter she should follow his orders!
So taraweeh prayer as a nafl or sunnah prayer has at least the same level of tawab or prescription for women, even if scholars (especially those who say that a woman should pray at home) say it's preferable for a woman to pray at home.
For the technical term: The Hanafi, Shafi'i and Hanbali school have defined it as sunnah muakkadah, while Maliki school call it mandubah. (Source fiqh according the 4 madhabs in Arabic)