The Rashi referenced in my answer there says in part:
אלו ערביים השוכנים באהלים במדברות ורועים מקנה כל ימיהם
These are the arabs that dwell in tents in the desert and pasture flocks all their lives.
So Rashi explicitly conflates the two.
Then again, arabs in Rashi's terminology might more mean desert dwellers rather than the modern definition of Arabs meaning a common cultural connection among a heterogeneous group of people that we think of today. Or perhaps Rashi means Arabians (people specifically from the Arabian peninsula).
So in modern terminology, Yishmoel's descendants may be Arabs today, but not all Arabs are descendants of Yishmoel - and given the degree that Islam in the area has pushed converts (by force or financial pressure), I would be surprised if they claimed real literal genetic decent from Yishmoel, rather than some sort of spiritual heritage.