Uber Eats seemed to be it's own thing, but now they seem to be tying them a bit more together. I've even seen the Uber app offering me the option to have food delivery setup while on my ride. Basically trying to give you the option to have food delivery arranged to show up to your destination around the same time you arrive.
But I believe you're right that initially they were more separate entities, but now it's kinda merged.
My initial claim only works for Uber Eats. It can only be used for ordering food. There's a button to order a ride but it redirects to the Uber app.