Why does a bump/normal map change the look of a plane to which they're applied to, even if the plane only has 1 normal? From my understanding, a normal map makes the existing normals on a mesh to change the direction they point in, to fake the illusion of grooves/depth/scratches,etc. So the more polygons you have = more normals = the better the effect from the normal map
A bump map from my understanding takes the normals on a mesh and scale them, unlike normal maps which can only change the direction the normals point in
Yet I noted that when I did the below to create a procedural bump map,

A bumpy effect is created. How is this possible? There is only one normal on this plane so how do I get a bumpy effect all throughout the plane? (I also noted that after removing the bump map node from Principled BSDF, the normal of the plane flipped directions
And when I tried the below to create a procedural normal map,

Sure, no longer is there a bump effect, but a pattern-like color effect is present somehow
My question is, how is that in both these cases, bump and normal maps, maps that only affect the scale/direction of your normal, create a drastic bumpy effect/pattern-color effect on a mesh with only one single normal?
A normal can be thought of as the direction a face is pointing.  The face (usually) has one normal, it's just a vector pointing into space going outwards from the face.  For our purposes here, it defines the average angle of reflection of light rays.
When you modify it with a Normal Map, you're giving it additional instructions on how to handle light across the face.  For every evaluated pixel, the light is taking the face normal and your Normal Map information into account.
So it's not that it is creating more normals.  There is only one, with a little math being done for every pixel sampled.  Very easy for your processor/gpu.
From Wikipedia

To calculate the Lambertian (diffuse) lighting of a surface, the unit
vector from the shading point to the light source is dotted with the
unit vector normal to that surface, and the result is the intensity of
the light on that surface. Imagine a polygonal model of a sphere - you
can only approximate the shape of the surface. By using a 3-channel
bitmap textured across the model, more detailed normal vector
information can be encoded. Each channel in the bitmap corresponds to
a spatial dimension (X, Y and Z). This adds much more detail to the
surface of a model, especially in conjunction with advanced lighting
techniques.