Vertices do not follow the shape of the object after subdivision surface and changed to edit mode

Question

Why don't the vertices follow the shape of the mesh item itself when I added subdivision surface.

Answer 1

A modifier doesn't modify the topology for real, it only does it virtually, if you go in Edit mode you'll see the mesh as it really is, not as virtually modified by the modifier. If you want to modify the mesh for real you need to apply the modifier:

But if you want to keep the modifier (because you don't need to, for example a Subdivision Surface modifier is better to keep because it keeps the topology light, while applying it will make the topology heavier), and if you want to see the mesh as it would be if you applied it, enable the On Cage option (you still won't see the virtual faces, only the existing one as modified by the modifier):