Is it OK to call Mexicans "Native Americans?"?

Yesterday I was at a birthday party for my step-granddaughter, who turned 9. There were a bunch of other kids there, all different colors.
After they’d eaten their cake and ice cream they all ran off to play. One kid had left her paper plate and bowl in the driveway, where she’d been sitting. My step-daughter saw it, asked whose it was.
I thought about the order that the girls had been sitting in and I said, “It was the Indian girl.”
My step-daughter said, “She’s Mexican,” and her tone of voice implied, “Duh.”
I said, “Same diff.”
My step-daughter just shook her head, like there is some big, obvious difference between a Mexican and a Native American, which there isn’t. They’re the same base race.