About Arab and early muslims

Assalamualaikum, I was reading" seeing Islam as others saw it" book but I noticed that arabs are constantly called as tayy but tayy is a clanas I know prophet was Quraish and amir al muminin were also Quraish but why they were never called as Quraish but Tayy?Is Quraish a clan of tayy tribe?

I read qusay is in the lineage but if that is the root is the noun named Tayy then maybe someone else can help...insha Allaah