I don't think there are any Tuigan living in the Raurin desert; Raurin is southeast of Mulhorand, and the Endless Waste, where the Tuigan dwell, is far to the north of that. The Horde boxed set says the Tuigan have very little contact with elves and tend to treat them like subhuman beasts when they do.
Al Qadim means "the ancient" or "the old" in Arabic. Qahara doesn't seem to be a real Arabic word (at least, it's not in this dictionary
). Al Qahira is the Arabic name for Cairo, Egypt.
The Forgotten Realms Campaign Guide
says the elves of Al Qahara "have strangely weathered features" and favor flowing, colorful gowns for adults and loose pants and simple tunics for children. They revere the desert as normal elves do the forests, seeing it as a place of beauty and wild majesty as well as cruelty. They're generous with food and lodging and eager to trade. Desert elves seem like a good match.
I don't think earlier editions mentioned elves in the Raurin Desert at all, and honestly it's weird that the only sentient race the 4th edition campaign guide mentions in Raurin is elves (plus a tiefling). I think there are supposed to be humans there as well, but 4th edition doesn't describe them. First edition's Desert of Desolation
mentioned a human ethnic group called the Raurindi, presumably descended from the Mulan, as they venerate the Mulhorandi pantheon (though they're said to venerate all religions as sacred) when they haven't converted to the worship of the Adama
(which Desert of Desolation
interprets as a monotheistic deity called Anu instead of the pantheistic belief of later editions). They seem more isolationist than the elves, disliking strangers though generous to those who have proven themselves their friends. They're described as hot-tempered, emotional, somber, pessimistic, and bad-mannered, and they swear vendettas against those who defile their tombs and holy places.
says that Raurin is inhabited by mongrelmen and human nomads, with no other details except the Mulhorandi gods seem to be worshiped there (Set is noted in particular, but priests of Thoth and Anhur also seem familiar with the area). There's no mention of elves.
Both the Raurindi and the desert elves should be vaguely Arabic-Egyptian in culture.