Anyway, corner points are what we mathematicians normally call "vertices." You can think of a vertex as the end point shared by two line segments or rays.
It's important to understand that squares, circles, and other geometric shapes are defined as infinite sets of points in a space of some kind like a plane. Like any two sets, two geometric shapes can share elements, and their elements are points. A point shared by two geometric shapes is called an "intersection point" because it's an element in the intersection of the two sets of points that make up the two shapes. So if a point is a vertex on a triangle, for example, then that same point can also be an element of a set that makes up a circle. It is a "corner point on or in a circle" that is an element of both sets.
I recommend you study basic trigonometry and set theory for more information.