How to activate individual point snapping in Blender?

Question

3D

Is it possible to snap points to a polygon individually?
Those. so that not the center of the selected vertices sticks to the polygon, but each vertex is individually snapped
Source objects

snapping result

desired result

Answer 1

I think you need the Shrinkwrap modifier. He knows how to project one object onto another.
Blend file with an example.

Answer 2

If you need to stick vertices, try switching to vertex selection mode.

Answer 3

If you need just such a shape, flattened to a plane. Then type SZ 0 Enter.